Find all intercepts of the following function.
$f ( x ) = \frac { 4 x ^ { 2 } - 6 x + 6 } { x - 4 }$
A)y-intercept: $\left( 0 , - \frac { 3 } { 2 } \right)$
B)y-intercept: $\left( \frac { 3 } { 2 } , 0 \right)$
C)y-intercept: (0, 3)
D)Intercept: (0, 0)
E)x-intercept: $\left( - \frac { 3 } { 2 } , 0 \right)$

Question

Find all intercepts of the following function. 
 $f ( x ) = \frac { 4 x ^ { 2 } - 6 x + 6 } { x - 4 }$  
A)y-intercept: $\left( 0 , - \frac { 3 } { 2 } \right)$
B)y-intercept: $\left( \frac { 3 } { 2 } , 0 \right)$
C)y-intercept: (0, 3)
D)Intercept: (0, 0)
E)x-intercept: $\left( - \frac { 3 } { 2 } , 0 \right)$

Quizplus · Accepted Answer

To find the y-intercept, substitute $x = 0$ into the function: $f(0) = \frac{4(0)^2 - 6(0) + 6}{0 - 4} = \frac{6}{-4} = -\frac{3}{2}$. Thus, the y-intercept is $\left(0, -\frac{3}{2}\right)$. There are no x-intercepts because the numerator $4x^2 - 6x + 6$ does not have real roots (its discriminant $b^2 - 4ac = (-6)^2 - 4(4)(6) < 0$).

Find All Intercepts of the Following Function f(x)=4x2−6x+6x−4f ( x ) = \frac { 4 x ^ { 2 } - 6 x + 6 } { x - 4 }f(x)=x−44x2−6x+6​

Find All Intercepts of the Following Function $f ( x ) = \frac { 4 x ^ { 2 } - 6 x + 6 } { x - 4 }$