EOC Functions (Linear vs Exponential)

Linear functions have the equation y = mx + b. Which two statements are true about these functions?

• The dependent variable changes the same amount for equal intervals of the independent variable

• The y variable changes the same amount for equal intervals of the x variable

• The dependent variable changes the same percent rate for equal intervals of the independent variable

• The y variable changes the same percent rate for equal intervals of the x variable

Answer explanation

Y = dependent variable

X = independent variable

Tags

CCSS.HSF-LE.A.1B

Exponential functions have the equation y = a(b)^x. Which two statements are true about these functions?

• The dependent variable changes the same amount for equal intervals of the independent variable

• The y variable changes the same amount for equal intervals of the x variable

• The dependent variable changes the same percent rate for equal intervals of the independent variable

• The y variable changes the same percent rate for equal intervals of the x variable

Answer explanation

Y = dependent variable

X = independent variable

Tags

CCSS.HSF-IF.C.8B

What type of function does the table represent?

• Linear

• Exponential

• Neither

Answer explanation

Linear Functions

Subtract y values backwards

Differences will be the same

Change will be same number

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Exponential Functions

Subtract y values backwards

Differences will be different

Divide the differences

Change will be same %

What type of function does the table represent?

• Linear

• Exponential

• Neither

Answer explanation

Which scatter plot BEST represents a model of exponential growth?

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Tags

CCSS.HSF-IF.C.7E

Which table represents an exponential function?

(anchor chart picture with arrow reminds you to divide y values backwards)

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Answer explanation

This is the only exponential function from the options

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Divide y values backwards

This will produce same result

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243 /81 = 3

81 / 27 = 3

27 / 9 = 3

9 / 3 = 3

A table of values is shown for f(x) and g(x).

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Which statement compares the graphs of f(x) and g(x) over the interval [0, 5]?

• The graph of f(x) always exceeds the graph of g(x) over the interval [0, 5]

• The graph of g(x) always exceeds the graph of f(x) over the interval [0, 5]

• The graph of g(x) exceeds the graph of f(x) over the interval [0, 4], the graphs intersect at a point between 4 and 5, and then the graph of f(x) exceeds the graph of g(x)

• The graph of f(x) exceeds the graph of g(x) over the interval [0, 4], the graphs intersect at a point between 4 and 5, and then the graph of g(x) exceeds the graph of f(x)

Answer explanation

For x values between 0 and 4:

- F(x) has higher y-values

- G(x) has lower y-values

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For x values 5 and above:

- F(x) has lower y-values

- G(x) has higher y-values

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On interval (4, 5):

- Both functions must have crossed paths (this means they "intersected"), so that G(x) will become greater

Tags

CCSS.HSF-IF.C.7D

Which statement is true about the graphs of exponential functions?

• The graphs of exponential functions never exceed the graphs of linear and quadratic functions

• The graphs of exponential functions always exceed the graphs of linear and quadratic functions

• The graphs of exponential functions eventually exceed the graphs of linear and quadratic functions

• The graphs of exponential functions eventually exceed the graphs of linear functions but not quadratic functions

Answer explanation

An example is shown to prove the statement

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H(x) is linear

G(x) is quadratic

F(x) is exponential

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It is possible for the exponential function to not be greatest at the start

However, at high x-values on the right of the graph, the exponential function will be greater than other functions

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Lamar measures the temperature outside and the number of cricket chirps. He found a linear relationship where the warmer it is outside, the more a cricket will chirp.

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Use the data collected to create a linear relationship that models the number of cricket chirps, C, as a function of temperature, t.

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Answer explanation