AnswersAlgebraic ReasoningUsing Exponential Functions — QuizQuestion 21
21
QuizMultiple Choice

Using Exponential Functions — Quiz

Question 21 • Algebraic Reasoning

Determine which of the following graphs represent the equation. Also determine the y -intercept of the graph. y is equal to 5 times open paren 2 to the x th power close paren

Answer
A
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. The y-intercept of the graph is 2. y -intercept is equal to 2
B
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 3 1), (negative 3 comma 0 point 6 2 5), (negative 2 comma 1 point 2 5), (negative 1 comma 2 point 5), and (0 comma 5). The y-intercept of the graph is 5. y -intercept is equal to 5
C
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 2 5), (negative 1 comma 0 point 5), (0 comma 1), (1 comma 2), and (2 comma 4). The y-intercept of the graph is 1. y -intercept is equal to 1
D
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. The y-intercept of the graph is 1. y -intercept is equal to 1

Explanation

The equation is y = 5(2^x). At the y-intercept, x = 0, so y = 5(2^0) = 5. The graph also passes through points such as (−1, 2.5) and (−2, 1.25), matching choice B, whose y-intercept is 5.

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