Calculus Examples

$y = {(x - 7)}^{5}$

Step 1

Find the x-intercepts.

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Step 1.1

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

$0 = {(x - 7)}^{5}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as ${(x - 7)}^{5} = 0$ .

${(x - 7)}^{5} = 0$

Step 1.2.2

Set the $x - 7$ equal to $0$ .

$x - 7 = 0$

Step 1.2.3

Add $7$ to both sides of the equation.

$x = 7$

Step 1.3

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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Step 2.1

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

$y = {((0) - 7)}^{5}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = {(0 - 7)}^{5}$

Step 2.2.2

Remove parentheses.

$y = {((0) - 7)}^{5}$

Step 2.2.3

Simplify ${((0) - 7)}^{5}$ .

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Step 2.2.3.1

Subtract $7$ from $0$ .

$y = {(- 7)}^{5}$

Step 2.2.3.2

Raise $- 7$ to the power of $5$ .

$y = - 16807$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 16807)$

Step 3

List the intersections.

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

y-intercept(s): $(0, - 16807)$

Step 4