Question

Please help very important ‼️‼️‼️

Answer 1

Answers:

X-intercept:

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

Y-intercept:

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

Explanation:

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

X-intercept:

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)`

Y-intercept:

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)`