Find the x and y Intercepts f(x)=-|x|+7

$f (x) = - | x | + 7$

Step 1

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = - | x | + 7$

Solve the equation.

Rewrite the equation as $- | x | + 7 = 0$ .

$- | x | + 7 = 0$

Subtract $7$ from both sides of the equation.

$- | x | = - 7$

Divide each term in $- | x | = - 7$ by $- 1$ and simplify.

Divide each term in $- | x | = - 7$ by $- 1$ .

$\frac{- | x |}{- 1} = \frac{- 7}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{| x |}{1} = \frac{- 7}{- 1}$

Divide $| x |$ by $1$ .

$| x | = \frac{- 7}{- 1}$

Simplify the right side.

Divide $- 7$ by $- 1$ .

$| x | = 7$

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$x = \pm 7$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 7$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 7$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 7, - 7$

x-intercept(s) in point form.

x-intercept(s): $(7, 0), (- 7, 0)$

Step 2

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = - | 0 | + 7$

Simplify $- | 0 | + 7$ .

Simplify each term.

The absolute value is the distance between a number and zero. The distance between $0$ and $0$ is $0$ .

$y = - 0 + 7$

Multiply $- 1$ by $0$ .

$y = 0 + 7$

Add $0$ and $7$ .

$y = 7$

y-intercept(s) in point form.

y-intercept(s): $(0, 7)$

Step 3

List the intersections.

x-intercept(s): $(7, 0), (- 7, 0)$

y-intercept(s): $(0, 7)$

Step 4

Find the x and y Intercepts f(x)=-|x|+7

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