Using Exponential Functions — Quiz

Question 2 • Algebraic Reasoning

Determine which of the following graphs represent the equation. Also determine the y -intercept of the graph. y is equal to 3 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 0 7 4), (negative 2 comma 0 point 2 2), (negative 1 comma 0 point 6 6), 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 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 4 comma 0 point 1 8 7 5), (negative 3 comma 0 point 3 7 5), (negative 2 comma 0 point 7 5), (negative 1 comma 1 point 5), and (0 comma 3). The y-intercept of the graph is 3. y -intercept is equal to 3

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

To find the y-intercept, set x = 0: y = 3(2⁰) = 3. The graph also has values 1.5 at x = −1, 0.75 at x = −2, and 0.1875 at x = −4, matching the points in choice C. Therefore, choice C represents the equation, and its y-intercept is 3.

AI-written and checked against the verified answer.

More from this Course

Quiz

Quiz

Quiz