Using Exponential Functions — Quiz

Question 13 • Algebraic Reasoning

Determine which of the following graphs represent the equation. Also determine the y -intercept of the graph. y is equal to 4 times open paren 2 to the x th power close paren

Answer

Image with description A coordinate plane has an x-axis ranging from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. The graph increases as x values move from left to right and the graph passes through the points (negative 3 comma 0 point 1 2 5), (negative 2 comma 0 point 2 5), (negative 1 comma 0 point 5), and (0 comma 1). The y-intercept of the graph is 1. y -intercept is equal to 1

Image with description A coordinate plane has an x-axis ranging from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. The graph increases as x values move from left to right and the graph passes through the points (negative 2 comma 0 point 1 2 5), (negative 1 comma 0 point 5), and (0 comma 2). The y-intercept of the graph is 2. y -intercept is equal to 2

Image with description A coordinate plane has an x-axis ranging from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. The graph increases as x values move from left to right and the graph passes through the points (negative 4 comma 0 point 2 5), (negative 3 comma 0 point 5), (negative 2 comma 1), (negative 1 comma 2), and (0 comma 4). The y-intercept of the graph is 4. y -intercept is equal to 4

Image with description A coordinate plane has an x-axis ranging from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. The graph increases as x values move from left to right and the graph passes through the points (negative 2 comma 0 point 0 6 2 5), (negative 1 comma 0 point 1 2 5), and (0 comma 1). The y-intercept of the graph is 1. y -intercept is equal to 1

Explanation

For y = 4(2^x), substitute x = 0 to find the y-intercept: y = 4(2^0) = 4. The graph also has values 2, 1, and 0.5 at x = −1, −2, and −3, respectively, matching choice A. The y-intercept is 4.

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