Free Printable Algebra 1: Topic 6(Exponential Functions)

1.

Solve

$\left(4^{\frac{x}{2}}\right)\left(4^{\frac{x}{5}}\right)=4^{14}$

a)

15

b)

20

c)

5

d)

3/5

2.

Solve
$\left(2^{2x+2}\right)\left(2^{3x-7}\right)=2^{25}$

a)

6

b)

3

c)

1

d)

5

3.

$\left(5^{\frac{x}{3}}\right)\ \left(5^{\frac{x}{4}}\right)\ =\ 5^5$ Solve the equation

a)

x = 7

b)

x = 20

c)

$x\ =\ \frac{60}{7}$

d)

$x\ =\ \frac{7}{60}$

4.

Solve the following now!

\left(\frac{1}{4}\right)^{x-2}=64

a)

$x=6$

b)

$x=5$

c)

$x=-2$

d)

$x=-1$

5.

Solve the following using your laws of exponents.

3^{2x-1}=27

a)

Not here

b)

$x=\frac{3}{2}$

c)

$x=1$

d)

$x=2$

6.

What is the equation that best represents the graph?

a)

y=2^y

b)

y=2^x

c)

y=2^-x

d)

y=x²

7.

What is the domain and range of the function y=2^x?

Use the graph to help!

a)

Domain: All Real Numbers

Range: y>0

b)

Domain: All Real Numbers

Range: y>1

c)

Domain: −2<x

Range: y>0

d)

Domain: All Real Numbers

Range: y>0

8.

Given y=3^xdetermine the y-intercept

a)

(0,1)

b)

(0,3)

c)

No Y-intercept

d)

y=1

9.

What is the horizontal asymptote for the graph of

f(x)=13(0.5)^x?

a)

y=0.5

b)

y=13

c)

y=6

d)

y=0

10.

For $f\left(x\right)=4\cdot3^x$ , find the correct graph, asymptote, domain and range.

a)

b)

11.

For $f\left(x\right)=3^x$ , find the correct graph, asymptote, domain and range.

a)

b)

12.

Given the function $y=3\left(2\right)^x$ , fill in the blank in the table when $x=5$ .

a)

96

b)

7776

c)

30

d)

$-30$

13.

Which is the best graph for $f\left(x\right)=-3^x$ ?

a)

b)

c)

d)

14.

Which graph represents $y=\frac{1}{2}\cdot4^x$

a)

b)

c)

d)

15.

This is an example of.....

a)

exponential decay

b)

exponential growth

c)

constant change

d)

a linear function

16.

What function is present?

a)

Absolute Value

b)

Exponential Decay

c)

Linear Equation

d)

Exponential Growth

17.

Which of the equations below represent this table?

a)

y=3⋅(36)^x

b)

y=36⋅(3)^x

c)

y=3⋅(⅓)^x

d)

y=36⋅(⅓)^x

18.

Write the equation of the table.

a)

y=4(4)^x

b)

y=4(2.68)^x

c)

y=4(1+1.67)^x

d)

y=4(1.67)^x

19.

Write an exponential function in the form y=ab^x that goes through points (0,9) and (3,72).

a)

y=9(3)^x

b)

y=2(9)^x

c)

y=9(2)^x

d)

y=8(3)^x

20.

Determine the exponential equation for the graph.

a)

$f\left(x\right)=2\left(3\right)^x$

b)

$f\left(x\right)=4\left(2\right)^x$

c)

$f\left(x\right)=3\left(2\right)^x$

d)

$f\left(x\right)=3\left(3\right)^x$

21.

In an exponential function, what does the 'a' represent?

a)

Slope

b)

Rate of change

c)

Y-intercept

d)

Multiplier

22.

What is it about the equation y = 2(9/7)^x that indicates that it is a model for exponential growth?

a)

The equation is growth because 2 is positive.

b)

The equation is growth because the factor is positive.

c)

The equation is growth because the factor is greater than one.

d)

The equation is growth because the exponent is always positive.

23.

Consider the equation y=200(1.08)^x which models the increase in value of an autographed Annie program. Let y = the value of the item, let x = the number of years since the performance. What does the 1.08 in the equation indicate?

a)

The value of the item is increasing by $1.08 each year.

b)

The value of the item is increasing by 1.08% each year.

c)

The value of the item will increase to $200 1.08 years after purchase.

d)

The value of the item is increasing by 8% each year.

24.

A population of mutant venus fly trap plants are taking over an island in the South Pacific, capturing everything from insects to small rodents. When they were first discovered they covered 4 square kilometers. As the population grows, the plants spread and cover more land. Use the table to write an equation.

a)

y=4(4)^x

b)

y=4(2.68)^x

c)

y=4(1+1.67)^x

d)

y=4(1.67)^x

25.

Your 3 year investment of $20,000 received 5.2% interest compounded annually. What will your total balance be at the end?

a)

$23,285.05

b)

$3,285.05

c)

$2,385

d)

$32,285

26.

The Arnold's took out a loan for $195,000 to purchase a home. At a 4.3% interest rate compounded annually, how much interest will they have paid over the course of 30 years?

a)

$494,546.99

b)

$529.305.61

c)

$689,546.99

d)

$640,891.53

27.

Emma deposits $1200 into an account that pays 3% interest, compounded monthly. What is her ending balance after one year?

a)

$1,613.87

b)

$1,709.91

c)

$1,236.50

d)

$1,203.00

28.

A population of humpback whales has 6,500 whales. Their population is declining such that only 94% of the number of whales remain from the year before. Choose the equation that matches this situation:

a)

$y=6,500\left(1.94\right)^x$

b)

$y=6,500\left(94\%\right)^x$

c)

$y=6,500\left(0.94\right)^x$

d)

$y=0.94\left(6,500\right)^x$

29.

The population of Townville is decreasing at a rate of 6% each year. If the starting population was 7,000 what equation represents the current population after x number of years?

a)

$f\left(x\right)=7000\left(0.6\right)^x$

b)

$f\left(x\right)=7000\left(0.4\right)^x$

c)

$f\left(x\right)=7000\left(0.06\right)^x$

d)

$f\left(x\right)=7000\left(0.94\right)^x$

30.

What is the transformation?

a)

Vertical Translation up 1

b)

Vertical Translation down 1

c)

Horizontal Translation left 1

d)

Horizontal Translation right 1

31.

What is the transformation?

a)

Vertical Translation up 2

b)

Vertical Translation down 2

c)

Horizontal Translation left 2

d)

Horizontal Translation right 2

32.

How has the function $3^x-5$ been transformed from the parent function $3^x$ ?

a)

Shifted up 5

b)

Shifted down 5

c)

Reflection over the x-axis

d)

Reflection over the y-axis

33.

a)

$y=4^{\left(x-2\right)}$

b)

$y=4^x-2$

c)

$y=4^x+2$

d)

$y=4^{\left(x+2\right)}$

34.

Using the parent function y=3^x what would the graph of y=3^x+1 look like?

a)

Horizontal shift left one unit

b)

Horizontal shift right one unit

c)

Vertical shift up one unit

d)

Vertical shift down one unit

35.

What is the asymptote of y = 2^x - 3

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

36.

What is the horizontal asymptote of the exponential function?

a)

y = 0

b)

y = -1

c)

x = 0

d)

x = -1

37.

What is the transformation?

a)

Vertical Translation up 2 and Horizontal translation right 1

b)

Vertical Translation down 2 and Horizontal Translation left 1

c)

Horizontal Translation left 2 and Vertical Translation up 1

d)

Horizontal Translation right 2 and Vertical Translation down 1

38.

What transformations have happened to y = 2^x if the new equation is

y = 2^(x+3) -6

a)

It stayed the same

b)

up 3, left 6

c)

right 3, down 6

d)

left 3, down 6

39.

Which of the following function best represents this graph?

a)

$f\left(x\right)=2^x+2$

b)

$f\left(x\right)=-2^x+2$

c)

$f\left(x\right)=-2^x-2$

d)

$f\left(x\right)=0.5^x+2$

40.

Which graph best represents a parent function that has shifted up 5 units?

a)

b)

c)

d)

41.

Solve the following exponential equation:
$9^{8-x}=27^{x-3}$

a)

$x=5$

b)

$x=-5$

c)

$x=\frac{1}{5}$

d)

$x=-\frac{1}{5}$

42.

How would you solve an exponential equation like the one below:
$4^{2x-3}=4^{6x+5}$

a)

Rewrite $4$ as $2^2$

b)

Multiply the exponents

c)

Set the exponents equal to each other

d)

Add the exponents

43.

Which of the following function best represents this graph?

a)

$g\left(x\right)=2^x+2$

b)

$k\left(x\right)=-2^x+2$

c)

$m\left(x\right)=-2^x-2$

d)

$f\left(x\right)=0.5^x+2$

44.

Which equation matches the graph?

a)

y = 2^x+3

b)

y = 2^x + 3

c)

y = 2^x

d)

y = 2^-x

45.

Which exponential equation could represent the graph shown?

a)

$f\left(x\right)=3^{\left(x-3\right)}-2$

b)

$f\left(x\right)=3^{\left(x+3\right)}-2$

c)

$f\left(x\right)=3^{\left(x-2\right)}-3$

d)

$f\left(x\right)=3^{\left(x+2\right)}-3$

46.

Which of the following equations represents exponential decay?

a)

y = 5(-0.7)^x

b)

y = 5(0.7)^x

c)

y = 5(2)^x

d)

y = 5(1.3)^x

47.

What is the y-intercept of the function y = 4(2)^x?

a)

(0, 4)

b)

(0, 0)

c)

(0, 2)

d)

(0, 8)

48.

Which transformation occurs when the equation y = 2^x is changed to y = 2^x - 5?

a)

Horizontal translation left 5

b)

Horizontal translation right 5

c)

Vertical translation down 5

d)

Vertical translation up 5

49.

Imagine Grace and her friends Elijah, Kai, and Mason are observing the growth of bacteria in a lab experiment. The number of bacteria doubles every hour. What happens to the graph representing the number of bacteria over time?

a)

The graph showing the number of bacteria over time increases rapidly.

b)

The graph showing the number of bacteria over time decreases rapidly.

c)

The graph showing the number of bacteria over time oscillates.

d)

The graph showing the number of bacteria over time remains constant.

50.

Benjamin and Lily are working on a population growth model for their biology project. They notice that tweaking the coefficient in front of the exponential function representing population growth changes the graph. How does it change the graph?

a)

Changing the coefficient changes the color of the graph.

b)

Changing the coefficient has no effect on the graph.

c)

Changing the coefficient affects the horizontal shift of the graph.

d)

Changing the coefficient in front of the exponential function affects the vertical stretch or compression of the graph.

51.

Hey Priya, Harper, and Mason! Can you explain how shifting an exponential function vertically changes its graph?

a)

Shifting vertically changes the domain of the exponential function

b)

Shifting vertically changes the color of the exponential function

c)

Shifting an exponential function vertically changes its graph by moving it up or down based on the constant added or subtracted.

d)

Shifting vertically changes the rate of growth of the exponential function

52.

Imagine Liam and Arjun are working on a population growth model of a rare species, represented by an exponential function. How does shifting this model horizontally on a graph affect its representation?

a)

The impact of shifting an exponential function horizontally is that it changes the position of the graph along the x-axis without altering its shape or steepness.

b)

Shifting horizontally affects the domain of the exponential function

c)

Shifting horizontally alters the y-intercept of the exponential function

d)

Shifting horizontally changes the steepness of the exponential function

53.

Hey math wizards! Nora and Aria are debating about exponential functions. Can you help them out? What effect does reflecting an exponential function over the x-axis have on its graph?

a)

The graph is compressed vertically.

b)

The graph is shifted to the right.

c)

The graph is stretched horizontally.

d)

The graph is flipped vertically.

54.

Priya and William are debating about exponential functions. How does reflecting an exponential function over the y-axis change its graph?

a)

The graph rotates clockwise

b)

The graph shifts vertically

c)

The graph becomes steeper

d)

The graph is mirrored across the y-axis.

55.

Imagine Levi is presenting the sales data of his startup to his friends Oliver, Sophia, and Abigail. Explain how a combination of transformations affects the graph representing the exponential growth of his sales.

a)

A combination of transformations affects the graph representing the exponential growth of sales by altering its font style

b)

A combination of transformations affects the graph representing the exponential growth of sales by changing its color

c)

A combination of transformations affects the graph representing the exponential growth of sales by modifying its domain

d)

A combination of transformations affects the graph representing the exponential growth of sales by changing its position, orientation, and scale.

56.

Priya and William are debating about exponential functions. How does reflecting an exponential function over the y-axis change its graph?

a)

The graph rotates clockwise

b)

The graph shifts vertically

c)

The graph becomes steeper

d)

The graph is mirrored across the y-axis.

57.

Hey math wizards! Nora and Aria are debating about exponential functions. Can you help them out? What effect does reflecting an exponential function over the x-axis have on its graph?

a)

The graph is compressed vertically.

b)

The graph is shifted to the right.

c)

The graph is stretched horizontally.

d)

The graph is flipped vertically.

58.

Imagine Levi is presenting the sales data of his startup to his friends Oliver, Sophia, and Abigail. Explain how a combination of transformations affects the graph representing the exponential growth of his sales.

a)

A combination of transformations affects the graph representing the exponential growth of sales by altering its font style

b)

A combination of transformations affects the graph representing the exponential growth of sales by changing its color

c)

A combination of transformations affects the graph representing the exponential growth of sales by modifying its domain

d)

A combination of transformations affects the graph representing the exponential growth of sales by changing its position, orientation, and scale.

59.

Elijah and Hannah are debating about exponential functions. What happens to the domain and range of an exponential function when it undergoes transformations?

a)

The domain and range remain constant regardless of transformations.

b)

The domain and range switch places after transformations.

c)

Transformations only affect the domain, not the range.

d)

The domain and range of an exponential function can change based on the transformations applied.

60.

Olivia and her friends Liam, Arjun, and Benjamin are studying the growth of a mysterious bacteria culture in their lab. They graph the population over time and notice it follows an exponential trend. How can they determine the equation of this exponential growth from the graph?

a)

Apply the Pythagorean theorem to find the equation

b)

Use the slope-intercept form of a linear equation

c)

Count the number of asymptotes on the graph

d)

The correct answer for the question is to identify key points such as the initial value, base, and transformations, and then use these points to form the equation of the exponential growth.

61.

Write the exponential equation from the table.

a)

$y=3^x$

b)

$y=3\left(1\right)^x$

c)

$y=3\left(3\right)^x$

d)

$y=3x+1$

62.

Write the exponential equation

a)

$y=4\left(2\right)^x$

b)

$y=2\left(2\right)^x$

c)

$y=2^x$

d)

$y=2\left(4\right)^x$

63.

Write the exponential equation

a)

$y=16\left(\frac{1}{2}\right)^x$

b)

$y=4\left(2\right)^x$

c)

$y=2\left(\frac{1}{2}\right)^x$

d)

$y=4\left(\frac{1}{2}\right)^x$

64.

Write the exponential equation

a)

$y=18\left(\frac{1}{3}\right)^x$

b)

$y=2\left(\frac{2}{3}\right)^x$

c)

$y=2\left(\frac{1}{3}\right)^x$

d)

$y=2\left(1\ \frac{1}{3}\right)^x$

65.

a)

$y=3\left(5\right)^x$

b)

$y=\frac{3}{5}\left(5\right)^x$

c)

$y=\frac{3}{5}\left(\frac{1}{5}\right)^x$

d)

$y=3\left(\frac{1}{5}\right)^x$

Algebra 1: Topic 6(Exponential Functions)

Total questions: 65

Worksheet time: 3hrs 53mins

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