Pre-Algebra Examples

$f (x) = 2^{x - 3}$ evaluatef $(5)$

Step 1

Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote is $y = 0$ .

Horizontal Asymptote: $y = 0$

Step 2

Graph $5$ .

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Step 2.1

Remove parentheses.

$y = 5$

Step 2.2

Use the slope-intercept form to find the slope and y-intercept.

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Step 2.2.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2.2.2

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = 0$

$b = 5$

Step 2.2.3

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $0$

y-intercept: $(0, 5)$

Slope: $0$

y-intercept: $(0, 5)$

Step 2.3

Find two points on the line.

$\begin{array}{c} x & y \\ 0 & 5 \\ 1 & 5 \end{array}$

Step 2.4

Graph the line using the slope, y-intercept, and two points.

Slope: $0$

y-intercept: $(0, 5)$

$\begin{array}{c} x & y \\ 0 & 5 \\ 1 & 5 \end{array}$

Slope: $0$

y-intercept: $(0, 5)$

$\begin{array}{c} x & y \\ 0 & 5 \\ 1 & 5 \end{array}$

Step 3

Plot each graph on the same coordinate system.

$f (x) = 2^{x - 3}$

$5$

Step 4