Question

Find the x - and y -intercepts of the graph of the function f(x)=−2|x+5|+2 . Enter your answers as points, (a,b). Enter the x -intercepts in order of increasing x -value. If there are no x -intercepts, enter NA in both answer areas.

Answer 1

The given function is

f(x) = - 2|x+5| + 2

The x intercept is the value of x when f(x) = 0

Substituting f(x) = 0 into the function, we have

0 = - 2|x+5| + 2

Subtract 2 from both sides

0 - 2 = - 2|x+5| + 2 - 2

- 2 = - 2|x+5|

Divide both sides by - 2. It becomes

- 2/- 2 = - 2|x+5|/- 2

1 = |x+5|

x + 5 = 1 or x + 5 = - 1

x = 1 - 5 or x = - 1 - 5

x = - 4 or x = - 6

x intercepts are x = - 6, x = - 4

Writing the x intercepts as points, they are

(- 6, 0) and (- 4, 0)

The y intercept is the value of f(x) when x = 0

substituting x = 0 into the function, we have

f(0) = - 2|0+5| + 2

f(0) = - 2|5| + 2 = - 2(5) + 2 = - 10 + 2

f(0) = - 8

y intercept = (0, - 8)