Answer:
x-intercept is ([tex]- \frac{1}{2}, 0[/tex]) and y-intercept is ([tex]0, 2[/tex])
Step-by-step explanation:
How do we find the y-intercept of a function?
We solve the equation when x=0. Let's try that with [tex]y+2=4(x+1)[/tex]
First, let's simplify it so that it resembles [tex]y=mx+b[/tex] more noticeably
[tex]y = 4x + 4 - 2 \\y = 4x + 2[/tex]
Now let's plug in 0 for x to find the y-intercept:
[tex]y = 4\cdot 0 + 2\\y = 2[/tex]
How do we find the x-intercept of a function?
We solve the equation when y=0. Let's try this from the simplified equation we got ([tex]y = 4x + 2[/tex])
[tex]0 = 4x + 2\\-2 = 4x\\\frac{-2}{4} = x\\x = - \frac{1}{2}[/tex]
We must remind ourselves that all y-intercepts have an x that is equal to 0 and that all x-intercepts have a y equal to 0.
That means that our x-intercept will be ([tex]- \frac{1}{2}, 0[/tex]) and our y-intercept will be ([tex]0, 2[/tex])
This corresponds to the 3rd option counting from the left.
Good luck!
