Question

asked Sep 6, 2024 133k views

1 Answer

Andrew McKinlay · Answer 1 · 2024-09-10T07:26:13+0000

Answers:

$\displaystyle ((-7)/(4),\;0)$

$\displaystyle (0, \;(7)/(4) )$

We can also graph the function to find the intercepts. See attached.

To find the x-intercept, we need to find when the function, f(x), is equal to 0. Then we will solve.

Given:

$\displaystyle f(x)=(-3)/(-4x-4)+1$

Set equal to 0:

$\displaystyle 0=(-3)/(-4x-4)+1$

Subtract 1 from each side of the equation:

$\displaystyle -1=(-3)/(-4x-4)$

Multiply both sides of the equation by (-4x - 4):

$\displaystyle -1(-4x-4)=-3$

Distribute:

$\displaystyle 4x+4=-3$

Subtract 4 from both sides of the equation, then divide by 4.

$\displaystyle x\;intercept=((-7)/(4),\;\;0)$

To find the y-intercept, we need to find the value of f(x) when x is equal to 0.

Given:

$\displaystyle f(x)=(-3)/(-4x-4)+1$

Substitute 0:

$\displaystyle f(0)=(-3)/(-4(0)-4)+1$

Multiply and subtract:

$\displaystyle f(0)=(3)/(4)+1$

Add:

$\displaystyle f(0)=(7)/(4)$