CFU 7.6 : Exponential Function Transformations

Imagine Grace and her friends Elijah, Kai, and Mason are observing the growth of bacteria in a lab experiment. The number of bacteria doubles every hour. What happens to the graph representing the number of bacteria over time?

• The graph showing the number of bacteria over time increases rapidly.

• The graph showing the number of bacteria over time decreases rapidly.

• The graph showing the number of bacteria over time oscillates.

• The graph showing the number of bacteria over time remains constant.

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Benjamin and Lily are working on a population growth model for their biology project. They notice that tweaking the coefficient in front of the exponential function representing population growth changes the graph. How does it change the graph?

• Changing the coefficient changes the color of the graph.

• Changing the coefficient has no effect on the graph.

• Changing the coefficient affects the horizontal shift of the graph.

• Changing the coefficient in front of the exponential function affects the vertical stretch or compression of the graph.

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Hey Priya, Harper, and Mason! Can you explain how shifting an exponential function vertically changes its graph?

• Shifting vertically changes the domain of the exponential function

• Shifting vertically changes the color of the exponential function

• Shifting an exponential function vertically changes its graph by moving it up or down based on the constant added or subtracted.

• Shifting vertically changes the rate of growth of the exponential function

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Imagine Liam and Arjun are working on a population growth model of a rare species, represented by an exponential function. How does shifting this model horizontally on a graph affect its representation?

• The impact of shifting an exponential function horizontally is that it changes the position of the graph along the x-axis without altering its shape or steepness.

• Shifting horizontally affects the domain of the exponential function

• Shifting horizontally alters the y-intercept of the exponential function

• Shifting horizontally changes the steepness of the exponential function

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Hey math wizards! Nora and Aria are debating about exponential functions. Can you help them out? What effect does reflecting an exponential function over the x-axis have on its graph?

• The graph is compressed vertically.

• The graph is shifted to the right.

• The graph is stretched horizontally.

• The graph is flipped vertically.

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Priya and William are debating about exponential functions. How does reflecting an exponential function over the y-axis change its graph?

• The graph rotates clockwise

• The graph shifts vertically

• The graph becomes steeper

• The graph is mirrored across the y-axis.

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Hey Priya, Aiden, and Noah! Can you figure out what happens when we stretch or compress an exponential function in its transformation?

• Stretching or compressing an exponential function changes its amplitude vertically and its growth rate horizontally.

• Stretching an exponential function changes its domain vertically and its range horizontally.

• Compressing an exponential function changes its growth rate vertically and its amplitude horizontally.

• Stretching or compressing an exponential function changes its period vertically and its phase horizontally.

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Imagine Levi is presenting the sales data of his startup to his friends Oliver, Sophia, and Abigail. Explain how a combination of transformations affects the graph representing the exponential growth of his sales.

• A combination of transformations affects the graph representing the exponential growth of sales by altering its font style

• A combination of transformations affects the graph representing the exponential growth of sales by changing its color

• A combination of transformations affects the graph representing the exponential growth of sales by modifying its domain

• A combination of transformations affects the graph representing the exponential growth of sales by changing its position, orientation, and scale.

Elijah and Hannah are debating about exponential functions. What happens to the domain and range of an exponential function when it undergoes transformations?

• The domain and range remain constant regardless of transformations.

• The domain and range switch places after transformations.

• Transformations only affect the domain, not the range.

• The domain and range of an exponential function can change based on the transformations applied.

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Olivia and her friends Liam, Arjun, and Benjamin are studying the growth of a mysterious bacteria culture in their lab. They graph the population over time and notice it follows an exponential trend. How can they determine the equation of this exponential growth from the graph?

• Apply the Pythagorean theorem to find the equation

• Use the slope-intercept form of a linear equation

• Count the number of asymptotes on the graph

• The correct answer for the question is to identify key points such as the initial value, base, and transformations, and then use these points to form the equation of the exponential growth.

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