Exponential Graph Context

1. Which function’s graph has a y-intercept of 2?

The graph shows an exponential function. What is the equation of the function?

• Shift 2 units up

•  Shift 2 units down

• Shift 2 units left

• Shift 2 units right

• {0, 4, 10}

•  {4.25, 4, 12}

•  {4.25, 5, 12}

• All real numbers

• Both graphs have a y-intercept of (0, 1), and   $y=2^x$ is  steeper.

• Both graphs have a y-intercept of (0, 1), and   $y=5^x$  is steeper.

• Neither graph has a y-intercept.

The exponential function f(x) has a horizontal asymptote at y = 3. What is the end behavior of f(x)?

• As x decreases, f(x) approaches, but never reaches, 0. As x increases, f(x) increases.

• As x decreases, f(x) approaches, but never reaches, 3. As x increases, f(x) increases.

• As x decreases, f(x) approaches, but never reaches, 3. As x increases, f(x) decreases.

• As x decreases, f(x) decreases. As x increases, f(x) approaches, but never reaches, 3.

The graph models the amount of radioactive element present over the course of a 10-minute experiment. What is the average rate of change of the amount of the element over the 10-minute experiment?

• -0.2 g/min

• -1.8 g/min

• -2.0 g/min

• -5.0 g/min

Which statements are true about the graph of the exponential function f(x)? Select all that apply.

• The domain is all real numbers.

• The range is all real numbers.

• The asymptote is y = -1.

• The y-intercept is 3.

• The x-intercept is 2.

Tina was observing the changing heights of a ball as it bounced over time. She graphed the function on this coordinate grid to show f(x), the height of the dropped ball, in feet, after its xth bounce.

Find f(3). Explain what this value represents in the given context.

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1. Tina was observing the changing heights of a ball as it bounced over time. She graphed the function on this coordinate grid to show f(x), the height of the dropped ball, in feet, after its xth bounce.

Tina said that a possible range for the given function is y > 0. Do you agree or disagree? If you agree, explain why the range is correct. If you disagree, what values should be the range for the given scenario?

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