Chapter 9: Q19. (page 597)

Graph each function. Find the y-intercept, and state the domain and range.
$y = 2 {(5)}^{x}$

Short Answer

Expert verified

The graph of the function is:

y-intercept is $(0, 2)$ and domain is all real number and range is $y > 0$ .

Step by step solution

Step 1. Graph the equation.

Graph of the function: $y = 2 {(5)}^{x}$

Step 2. Find the y-intercept.

The y-intercept of a graph is the point where the graph intersects the y-axis that is., x-coordinate of a y-intercept is 0. So, to find y-intercept substitute 0 for x into the equation $y = 2 {(5)}^{x}$ .

$y = 2 {(5)}^{x} = 2 {(5)}^{0} [x = 0] = 2$

Thus, y-intercept is $y = 2$ .

Step 3. Find the range and domain.

The domain of a function $f (x)$ is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.

From the graph, it can be concluded that domain is all real number and range is $y > 0$ .

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Graph each function. Find the y-intercept, and state the domain and range.
$y = 2 {(5)}^{x}$

Short Answer

Step by step solution

Step 1. Graph the equation.

Step 2. Find the y-intercept.

Step 3. Find the range and domain.

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Step by step solution

Step 1. Graph the equation.

Step 2. Find the y-intercept.

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One App. One Place for Learning.

Most popular questions from this chapter

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Graph each function. Find the y-intercept, and state the domain and range.
$y = 2 {(5)}^{x}$