Find the Y-intercepts and X-intercepts of F(X)

Question

f(X)= (X-3)³-5

Answer 1

f(x) = (x - 3)³ - 5

The x-intercept occurs at f(x) = 0

0 = (x - 3)³ - 5          set f(x) = 0

5 = (x - 3)³               add 5 to both sides

³√5 =x - 3                take cube root of both sides

3 + ³√5 = x

 

The y-intercept occurs at x = 0

f(x) = (0 - 3)³ - 5

f(x) = -27 - 5

f(x) = -32

Answer 2

f(x) = (x-3)³ - 5 

 

To find x intercept....set y = 0

f(x) = (x-3)³ - 5

0    = (x-3)³ - 5   add 5 to each side

5    = (x-3)³       now take the cube root of each side 

³√5  ^{= 3}√(x-3)³ 

³√5  = x-3

1.71  = x-3   add three to both sides

4.71 = x

So the x intercept is (4.71,0)

 

To find the y intercept....set x = 0

f(x) = (x-3)³ - 5

f(x) = (0-3)³ - 5

f(x) = -3³ - 5

f(x) = -27 - 5

f(x) = -32

So the y intercept is (0,-32)