Find the x and y Intercepts f(x)=(x^2-7x)/(x^2-64)

$f (x) = \frac{x^{2} - 7 x}{x^{2} - 64}$

Step 1

Find the x-intercepts.

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

$0 = \frac{x^{2} - 7 x}{x^{2} - 64}$

Solve the equation.

Set the numerator equal to zero.

$x^{2} - 7 x = 0$

Solve the equation for $x$ .

Factor $x$ out of $x^{2} - 7 x$ .

Factor $x$ out of $x^{2}$ .

$x \cdot x - 7 x = 0$

Factor $x$ out of $- 7 x$ .

$x \cdot x + x \cdot - 7 = 0$

Factor $x$ out of $x \cdot x + x \cdot - 7$ .

$x (x - 7) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x - 7 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x - 7$ equal to $0$ and solve for $x$ .

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

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

The final solution is all the values that make $x (x - 7) = 0$ true.

$x = 0, 7$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = \frac{{(0)}^{2} - 7 \cdot 0}{{(0)}^{2} - 64}$

Solve the equation.

Remove parentheses.

$y = \frac{0^{2} - 7 \cdot 0}{{(0)}^{2} - 64}$

Remove parentheses.

$y = \frac{0^{2} - 7 \cdot 0}{0^{2} - 64}$

Remove parentheses.

$y = \frac{{(0)}^{2} - 7 \cdot 0}{{(0)}^{2} - 64}$

Simplify $\frac{{(0)}^{2} - 7 \cdot 0}{{(0)}^{2} - 64}$ .

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$y = \frac{0 - 7 \cdot 0}{0^{2} - 64}$

Multiply $- 7$ by $0$ .

$y = \frac{0 + 0}{0^{2} - 64}$

Add $0$ and $0$ .

$y = \frac{0}{0^{2} - 64}$

Simplify the denominator.

Raising $0$ to any positive power yields $0$ .

$y = \frac{0}{0 - 64}$

Subtract $64$ from $0$ .

$y = \frac{0}{- 64}$

Divide $0$ by $- 64$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4

Find the x and y Intercepts f(x)=(x^2-7x)/(x^2-64)

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