Find the x and y Intercepts f(x)=(4x^2-4x)/(3x^2+4x-7)

$f (x) = \frac{4 x^{2} - 4 x}{3 x^{2} + 4 x - 7}$

Step 1

Find the x-intercepts.

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

$0 = \frac{4 x^{2} - 4 x}{3 x^{2} + 4 x - 7}$

Solve the equation.

Set the numerator equal to zero.

$4 x^{2} - 4 x = 0$

Solve the equation for $x$ .

Factor $4 x$ out of $4 x^{2} - 4 x$ .

Factor $4 x$ out of $4 x^{2}$ .

$4 x (x) - 4 x = 0$

Factor $4 x$ out of $- 4 x$ .

$4 x (x) + 4 x (- 1) = 0$

Factor $4 x$ out of $4 x (x) + 4 x (- 1)$ .

$4 x (x - 1) = 0$

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

$x = 0$

$x - 1 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

The final solution is all the values that make $4 x (x - 1) = 0$ true.

$x = 0, 1$

Exclude the solutions that do not make $0 = \frac{4 x^{2} - 4 x}{3 x^{2} + 4 x - 7}$ true.

$x = 0$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = \frac{4 {(0)}^{2} - 4 \cdot 0}{3 {(0)}^{2} + 4 (0) - 7}$

Solve the equation.

Remove parentheses.

$y = \frac{4 \cdot 0^{2} - 4 \cdot 0}{3 {(0)}^{2} + 4 (0) - 7}$

Remove parentheses.

$y = \frac{4 \cdot 0^{2} - 4 \cdot 0}{3 \cdot 0^{2} + 4 (0) - 7}$

Remove parentheses.

$y = \frac{4 {(0)}^{2} - 4 \cdot 0}{3 {(0)}^{2} + 4 (0) - 7}$

Simplify $\frac{4 {(0)}^{2} - 4 \cdot 0}{3 {(0)}^{2} + 4 (0) - 7}$ .

Simplify the numerator.

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

$y = \frac{4 \cdot 0 - 4 \cdot 0}{3 \cdot 0^{2} + 4 (0) - 7}$

Multiply $4$ by $0$ .

$y = \frac{0 - 4 \cdot 0}{3 \cdot 0^{2} + 4 (0) - 7}$

Multiply $- 4$ by $0$ .

$y = \frac{0 + 0}{3 \cdot 0^{2} + 4 (0) - 7}$

Add $0$ and $0$ .

$y = \frac{0}{3 \cdot 0^{2} + 4 (0) - 7}$

Simplify the denominator.

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

$y = \frac{0}{3 \cdot 0 + 4 (0) - 7}$

Multiply $3$ by $0$ .

$y = \frac{0}{0 + 4 (0) - 7}$

Multiply $4$ by $0$ .

$y = \frac{0}{0 + 0 - 7}$

Add $0$ and $0$ .

$y = \frac{0}{0 - 7}$

Subtract $7$ from $0$ .

$y = \frac{0}{- 7}$

Divide $0$ by $- 7$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4

Find the x and y Intercepts f(x)=(4x^2-4x)/(3x^2+4x-7)

Related Questions

Support LCMGCF.com by disabling your adblocker.