Chapter 9: Q45. (page 595)

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

Short Answer

Expert verified

The graph of the function is:

$y$ -intercept is $(0, 1)$ and domain is all real number and range is $y > 0$ .

Step by step solution

Step 1. Graph the equation.

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

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 $y = 2^{x}$ .

$\begin{array}{l} y = 2^{x} \\ = 2^{0} [x = 0] \\ = 1 \end{array}$

Thus, $y$ –intercept is $y = 1$ .

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.
$y = 2^{x}$

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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Graph each function. Find the y-intercept, and state the domain and range.y=2x

Short Answer

Step by step solution

Step 1. Graph the equation.

Step 2. Find the y-intercept.

Step 3. Find the range and domain.

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.
$y = 2^{x}$