Question

Which functions have a y-intercept that is greater than the y-intercept of the function g(x) = [X +31 + 4? Check three options

A. f(x) = -2 (x – 8)
B. h(x) = -5 |x| + 10
C. j(x) = -4(x + 2)2 + 8
D. k(x) = (x 4)2 + 4
E .m(x) = 4/x-8) +6

Answer 1

The options with y-intercepts greater than the y-intercept of g(x) = x + 31 + 4 are: Option A (f(x) = -2(x - 8), with a y-intercept of 16), Option D (k(x) = (x - 4)^2 + 4, with a y-intercept of 20), Option E (m(x) = 4/(x - 8) + 6, with a y-intercept of 5.5).

Step-by-step explanation:

To determine which functions have a y-intercept greater than g(x) = x + 31 + 4, we need to compare the y-intercepts of the given options with the y-intercept of g(x). The y-intercept of g(x) is the value of y when x = 0. Therefore, g(0) = 0 + 31 + 4 = 35.

Now, let's find the y-intercepts of the given options:

A. f(x) = -2(x - 8)
To find the y-intercept, substitute x = 0: f(0) = -2(0 - 8) = 16. The y-intercept is 16.

B. h(x) = -5|x| + 10
To find the y-intercept, substitute x = 0: h(0) = -5|0| + 10 = 10. The y-intercept is 10.

C. j(x) = -4(x + 2)^2 + 8
To find the y-intercept, substitute x = 0: j(0) = -4(0 + 2)^2 + 8 = -4(2)^2 + 8 = -4(4) + 8 = -16 + 8 = -8. The y-intercept is -8.

D. k(x) = (x - 4)^2 + 4
To find the y-intercept, substitute x = 0: k(0) = (0 - 4)^2 + 4 = (-4)^2 + 4 = 16 + 4 = 20. The y-intercept is 20.

E. m(x) = 4/(x - 8) + 6
To find the y-intercept, substitute x = 0: m(0) = 4/(0 - 8) + 6 = 4/(-8) + 6 = -1/2 + 6 = 5.5. The y-intercept is 5.5.

Therefore, the options with y-intercepts greater than the y-intercept of g(x) = x + 31 + 4 are:
Option A (f(x) = -2(x - 8), with a y-intercept of 16)
Option D (k(x) = (x - 4)^2 + 4, with a y-intercept of 20)
Option E (m(x) = 4/(x - 8) + 6, with a y-intercept of 5.5)