Graphing Exponential Functions

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

• Exponential Growth

• Exponential Decay

• Linear

• None

Answer explanation

The pictured graph shows a curve that is increasing at an accelerating rate, indicating exponential growth.

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CCSS.HSF.IF.B.4

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.3

Which of the following is an increasing exponential function whose y-intercept is 50?

• y = 50(.05)^x

• y = 50x - 4

• y = (2)^x + 50

• y = 50(1.4)^x

Answer explanation

The correct choice is y = 50(1.4)^x because it is the only increasing exponential function with a y-intercept of 50.

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CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.3

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CCSS.HSF.IF.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSF.LE.A.1

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CCSS.HSF.IF.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSF.LE.A.1

• Decay

• Growth

Answer explanation

The function represents exponential growth because the base (5) is greater than 1, and as x increases, y also increases.

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.B.5

• (3,0)

• (1/2, 0)

• (0,0)

• (0,3)

Answer explanation

The y-intercept of the graph of the exponential function y=3(1/2)^x is (0,3), as the y-intercept occurs when x=0 and y=3.

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CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What function is present? 

• Absolute Value

• Exponential Decay

• Linear Equation

• Exponential Growth

Answer explanation

The function present is Exponential Decay because it represents a decreasing quantity over time.

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CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

What is the y-intercept of the function?

• 2

• 3

• 1

• -2

Answer explanation

The y-intercept of the function is the value of y when x=0. In this case, the y-intercept is 3, so the correct answer is 3.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

• 2

• 3

• x

• y

Answer explanation

The base of the exponential function represented by the equation y=2(3)^x is 3.

Tags

CCSS.HSF.LE.B.5

• 4

• 7

• 0

• 1

Answer explanation

The slope of the linear equation y=4x+7 is 4, which is the coefficient of x in the equation.

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CCSS.HSS.ID.C.7