Diagnostic Quiz

Unit 9: Exponential Functions

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Multiple Choice

if $$y=2^x$$   what is y when x = 0, 2, 4?

• 1, 2 and 8

• 1, 4 and 16

• 0, 4 and 8

• 1, 2 and 8

Exponential Functions Intro

• Exponential Functions have the variable as an exponent

• The base can be any positive number

• The domain of exponential functions is always all real numbers

• the range for the parent is (0,∞)

• The parent function has a horizontal asymptote at y=0.

• The y-intercept is at (0,1)

Exponential Functions have a variable in the exponent

Multiple Choice

Which of the following is an exponential function?

• y = x²

• f(x) = 3x³

• $$y=\left(-2\right)^x$$  

• f(x) = 3^x

Vertical Transformations & Asymptote/Range

• If your graph is translated vertically, your asymptote and range will be affected

• Remember that the range for the parent function is (0,∞)

• The asymptote for the parent function is y=0

Multiple Choice

Identify the asymptote of the function $$-3\left(3\right)^x+4$$  

• y = -3

• y = 1

• y = 4

Multiple Choice

Determine the range for the function

f(x) = 3(2)^x-4 + 5

• [5,∞)

• (5,∞)

• [4,∞)

• (4,∞)

Multiple Choice

What is the range of this function?

• (-∞,0)

• (0,∞)

• (-∞,4)

• (4,∞)

Multiple Choice

The parent function  $$f\left(x\right)=3^x$$   is shown in red and is translated. What is the equation of the green graph?

• $$g\left(x\right)=3^x+2$$  

• $$g\left(x\right)=3^x-2$$  

• $$g\left(x\right)=3^{x-2}$$  

• $$g\left(x\right)=3^{x+2}$$  

Multiple Choice

How has the function $$7\left(3\right)^x-5$$ been transformed from the parent function  $$7\left(3\right)^x$$ ?

• Shifted up 5

• Shifted down 5

• Reflection over the x-axis

• Reflection over the y-axis

Multiple Choice

What is the domain of the function shown below?

• (-2,5)

• (0,12)

• $$\left(0,\infty\right)$$  

• All Real Numbers

Multiple Choice

Is this exponential growth or decay?

• Growth
• Decay

Multiple Choice

Is the graph linear, exponential or neither?

• Linear
• Exponential
• Neither

Multiple Choice

Is the pictured graph growth, decay, or linear or none?  

• Exponential Growth
• Exponential Decay
• Linear
• None

Multiple Choice

Pick the equation that is exponential growth

• y=2(0.5)^x
• y = 0.5(2)^x

Multiple Choice

Pick the equation that is exponential decay

• y=2000(0.88)
• y=0.5(1.88)

Multiple Choice

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

• SLOPE
• RATE OF CHANGE
• Y-INTERCEPT
• COMMON RATIO

Multiple Choice

What is the y -intercept of  y=3(4)^x?

• 1
• 0
• 4
• 3

Multiple Choice

What is the y-intercept of the function?

• 2
• 3
• 1
• -2

Multiple Choice

What is a, the starting term, for the function: f(x) = 300(1.16)^x?

• 300
• 1.16
• .16
• x

Multiple Choice

Given y=4^(x+1) determine the y-intercept

• (0,1)
• (0,4)
• (4,0)
• (1,0)

Multiple Choice

Given y=4^(x+1) determine the y-intercept

• (0,1)
• (0,4)
• (4,0)
• (1,0)

Multiple Choice

Is the table linear, exponential, or neither?

• Linear

• Exponential

• Neither

Multiple Choice

Is the table linear, exponential, or neither?

• Linear

• Exponential

• Neither

Multiple Choice

Is the table linear, exponential, or neither?

• Linear

• Exponential

• Nether

Multiple Choice

Is the table linear, exponential, or neither?

• Linear

• Exponential

• Neither

Multiple Choice

In the equation, y = mx + b, the letter b is the ___________.

• y-intercept
• x-intercept
• slope
• rate of change

Multiple Choice

Which form represents slope-intercept form?

• $$y=bx+m$$

• $$Ax+By=C$$

• $$y_2-y_1=m\left(x_2-x_1\right)$$

• $$y=mx+b$$

Multiple Choice

In the equation, y = mx + b, the letter m is the ___________.

• y-intercept

• x-intercept

• slope

• multiplier

Multiple Choice

Rewrite log₂8 = 3 in exponential form.

• 2⁸ = 3
• 2³ = 8
• 3² = 8
• 8³ = 2

Multiple Choice

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81
• log₈₁3 = 4
• log₃81 = 4
• log₄81 = 3

Multiple Choice

log₅25 = ?

• 2
• 5
• 125
• 10

Multiple Choice

Rewrite log_pt = m in exponential form.

• p^t = m
• t^m = p
• m^t = p
• p^m = t

Multiple Choice

Evaluate:
log₄16

• 2
• 4
• 1/2
• -2

Multiple Choice

Change to Exponential Form:
log₆36 = 2

• 2⁶=36
• 6²=36
• 36²=6
• 36⁶=2

Multiple Choice

ln(e^W)

• e
• W
• e^W
• undefined

Multiple Choice

log₅25 = ?

• 2
• 5
• 125
• 10

Multiple Choice

log (xy²)

• log (x)+2 log (y)

• log (x)+log (y²)

• log (x) - 2 log (y)

• log (x) + log (y) + log (2)

Multiple Choice

$$\log\left(\frac{x}{y}\right)$$  

• log (x) + log (y)

• x log (y)

• log (x-y)

• log (x) - log (y)

Multiple Choice

Expand  $$\log_4\left(6y\right)$$  

• $$\log_4\left(6\right)\ +\ \log_4\left(y\right)$$

• $$\log_4\left(6\right)\ -\ \log_4\left(y\right)$$

• $$y\log_4\left(6\right)\$$

• $$\log_4\left(\frac{6}{y}\right)\$$

Multiple Choice

Use properties of Logs to write  $$\log_3\left(6\right)+\log_3\left(2\right)$$  

as one Log

• $$\log_3\left(8\right)\$$

• $$\log_3\left(4\right)$$

• $$\log_3\left(12\right)$$

• $$\log_3\left(3\right)$$

Multiple Choice

f(x)=log₅(x+4) - 2

Find the Domain and Range

• Domain: x ≥ -4

  Range: all real numbers

• Domain: all real numbers

  Range: y ≥ -4

• Domain: all real numbers

  Range: y > -4

• Domain: x > -4

  Range: all real numbers

Multiple Choice

f(x)=log₅(x+4) - 2

Describe the transformation

• translation 4 units to the right, 2 units down

• translation 4 units to the left, 2 units down

• translation 4 units to the up, 2 units right

• translation 4 units to the up, 2 units left

Multiple Choice

What is the transformation of the logarithmic function
$$f\left(x\right)=\log\ \left(x+3\right)-1$$  

• left 3, right 1

• right 3, down 1

• right 3, up 1

• left 3, down 1

Multiple Choice

Which graph matches the function

*remember the transformation has shifted it right 3 and down 3