Precalculus Examples

$f (x) = | x | + 4$

Step 1

Find the x-intercepts.

Tap for more steps...

Step 1.1

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

$0 = | x | + 4$

Step 1.2

Solve the equation.

Tap for more steps...

Step 1.2.1

Rewrite the equation as $| x | + 4 = 0$ .

$| x | + 4 = 0$

Step 1.2.2

Subtract $4$ from both sides of the equation.

$| x | = - 4$

Step 1.2.3

There is no value of $x$ that makes the equation be true since an absolute value can never be negative.

No solution

Step 1.3

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

x-intercept(s): $None$

Step 2

Find the y-intercepts.

Tap for more steps...

Step 2.1

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

$y = | 0 | + 4$

Step 2.2

Simplify $| 0 | + 4$ .

Tap for more steps...

Step 2.2.1

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

$y = 0 + 4$

Step 2.2.2

Add $0$ and $4$ .

$y = 4$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 4)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 4)$

Step 4