Exponential Functions

What is the general shape of an exponential function?

• Perfect circle

• Sine wave pattern

• Straight line that intersects the x-axis

• Curve that starts at a positive value, increases rapidly, and never crosses the x-axis

How does changing the base affect the graph of an exponential function?

• Changing the base affects the graph of an exponential function by shifting it horizontally.

• Changing the base affects the graph of an exponential function by stretching or compressing it horizontally.

• Changing the base affects the graph of an exponential function by rotating it vertically.

• Changing the base affects the graph of an exponential function by changing the y-intercept.

Explain how a vertical stretch impacts the graph of an exponential function.

• The graph of the exponential function becomes flatter as it moves away from the x-axis.

• The graph of the exponential function becomes steeper as it moves away from the x-axis.

• The vertical stretch has no impact on the graph of an exponential function.

• The graph of the exponential function becomes a straight line.

Describe the effect of a vertical compression on the graph of an exponential function.

• The graph becomes narrower.

• The graph becomes wider.

• The graph shifts to the left.

• The graph shifts to the right.

What happens to the graph of an exponential function when there is a horizontal shift to the right?

• The graph of an exponential function becomes steeper.

• The graph of an exponential function shifts downwards.

• The graph of an exponential function remains unchanged.

• The graph of an exponential function shifts to the left.

Illustrate the impact of a horizontal shift to the left on the graph of an exponential function.

• The graph moves upwards.

• The impact of a horizontal shift to the left on the graph of an exponential function is that the graph moves to the right.

• The graph becomes steeper.

• The graph remains unchanged.

How does a reflection over the x-axis change the graph of an exponential function?

• The reflection over the x-axis changes the sign of the function's output.

• The reflection over the x-axis changes the function to a linear equation.

• The reflection over the x-axis changes the function to a quadratic equation.

• The reflection over the x-axis changes the function to a trigonometric function.

Explain the transformation caused by a reflection over the y-axis on the graph of an exponential function.

• The reflection over the y-axis shifts the exponential function up or down

• The reflection over the y-axis changes the concavity of the exponential function

• The reflection over the y-axis results in a mirror image of the original exponential function across the y-axis.

• The reflection over the y-axis results in a rotation of the exponential function

Solve the equation 2^x = 8 graphically.

• x = 3

• x = 5

• x = 2

• x = 4

Determine the solution to the equation 3^(x-1) = 27 using graphical methods.

• x = 4

• x = 3

• x = 5

• x = 2