Find all intercepts of the function. f(x)= -3+ sqrt(23-x^2)

Question

Find all intercepts of the function. f(x)= -3+ sqrt(23-x^2)

If there is more than one answer, enter them in a list separated by commas. Enter exact answers: decimal approximations will be marked incorrect. Your answers should be numbers, not ordered pairs.



Answer 1

To find the y-intercepts, you make x = 0. To find the x-intercepts, you make y = 0 (or f(x) = 0).

x-intercepts:

f(x) = -3 + sqrt(23 - x²)

0 = -3 + sqrt(23 - x²)

3 = sqrt(23 - x²)

3² = [sqrt(23 - x²)]²

9 = 23 - x²

x2 = 14

x = ±√14 (i.e., x = √14 and x = -√14)

So the x-intercepts are (√14, 0) and (-√14, 0) but they do not want ordered pairs so put x = √14 and x = -√14

y-intercept:

f(x) = -3 + sqrt(23 - x²)

f(0) = -3 + sqrt(23 - 0²)

f(0) = -3 + √23

So the y-intercept is (0, -3 + √23) but they do not want ordered pairs so put y (or f(x)) = -3 + √23