Question

Y = 2x

F(x) = -X^2 - 1
g(X) = X^2 + 5
Find the y-intercept and x-intercept for each function.

Answer 1

To find the y-intercept, set x=0 in the function; for x-intercept, set the function equal to 0. For Y=2x, both intercepts are at 0. F(x) and g(X) have y-intercepts at -1 and 5 respectively, with no real x-intercepts.

Step-by-step explanation:

To find the y-intercept and the x-intercept for the given functions, let's analyze each function separately:

• For Y = 2x:
  
  The y-intercept is found by setting x = 0, which gives Y = 2(0) = 0. So, the y-intercept is 0. The x-intercept is found by setting Y = 0, which solves to x = 0/2 = 0. So the x-intercept is also 0.
• For F(x) = -X^2 - 1:
  
  The y-intercept is found by setting x = 0, which gives F(0) = -(0)^2 - 1 = -1. So, the y-intercept is -1. The x-intercept is found by setting F(x) = 0, which solves to -X^2 - 1 = 0 or X^2 = -1, which has no real solutions. There are no x-intercepts.
• For g(X) = X^2 + 5:
  
  The y-intercept is found by setting x = 0, which gives g(0) = (0)^2 + 5 = 5. So, the y-intercept is 5. The x-intercept is found by setting g(X) = 0, which solves to X^2 + 5 = 0 or X^2 = -5, which also has no real solutions. There are no x-intercepts.