Chapter 6 Test Warm Up

Linear Functions...

are straight lines on a graph

Exponential Graphs

curve

Multiple Choice

Determine whether the graph is linear or exponential.

• Linear

• Exponential

Multiple Choice

Determine whether the graph is linear or exponential.

• Linear

• Exponential

Multiple Choice

Determine whether the graph is linear or exponential.

• Linear

• Exponential

Multiple Choice

Determine whether the graph is linear or exponential.

• Linear

• Exponential

​Is it Linear or Exponential?

​When given a table, look for a common difference or a common ratio.

​- If the pattern is add/subtract, the function is linear.

​- If the pattern is multiply/divide, the function is exponential.

​Examples:

Since the pattern is adding, the function is linear.

Since the pattern is multiplying, the function is exponential.

Multiple Choice

Is the pattern adding/subtracting or multiplying/dividing?

• adding/subtracting

• multiplying/dividing

Multiple Choice

Is this function linear or nonlinear?

• Linear

• Nonlinear

Multiple Choice

Is the function linear or exponential?

• linear

• exponential

Multiple Choice

Is this function linear or nonlinear?

• Linear

• Nonlinear

Product Rule 

When multiplying exponents with the same base

Multiple Choice

Simplify the expression.
x³x⁶

• x⁹

• x³

• x¹⁸

• x³⁶

Quotient Rule 

When dividing exponents with the same base

Multiple Choice

$$\frac{x^8}{x^5}$$  

• $$x^3$$  

• $$\frac{1}{x^3}$$  

• $$x^{13}$$  

• $$x^{40}$$  

Power to Power Rule 

When raising an exponent to another exponent

Multiple Choice

Simplify the following:
(x²y)⁵

• x⁷y⁵

• x²y⁵

• x¹⁰y⁵

• x⁵y⁵

Multiple Choice

Simplify the expression

(2ab)³

• 2³a³b³

• 2ab³

• 6a³b³

• 6ab

Multiple Choice

Simplify the following

$$\left(\frac{x^3}{y^4}\right)^2$$  

• $$\frac{x^5}{y^6}$$  

• $$\frac{x^6}{y^8}$$  

• $$\left(xy\right)^{234}$$  

Zero Exponent Rule

Multiple Choice

Simplify y⁰

• y

• 0

• 1

• 1y

Multiple Choice

Simplify -4x⁰

• -4x

• -4

• 1

• -1

Negative Exponent Rule

Multiple Choice

Write with positive exponents:

• a^-2

• a²

• $$\frac{1}{a^2}$$

• 2a

• y-intercept: (0,4)

• base: 5 

• exponential growth because the base 5 is greater than 1

Multiple Choice

What is the y-intercept represented by the equation e(x) = 10(5)^x

• (0,5)

• (5,0)

• (10,0)

• (0,10)

Multiple Choice

What is the y-intercept represented by the equation

$$f\left(x\right)=3\left(7\right)^x$$  

• (0,3)

• (3,0)

• (7,0)

• (0,7)

Multiple Choice

Suppose a culture of bacteria begins with 5000 cells and increases by 30% each year. Write an equation that represents this situation.

• y=5000(0.7)^x

• y=30(5000)^x

• y=5000(1.3)^x

• y=5000x^x