Question

Graph the square root functions and .

Which function has a y-intercept?

(1 point)

f(x)

g(x)

both f(x) and g(x)
What are the coordinates of the minimum point for the square root function that relates to the quadratic function f(x)=−3(x−5)2+7


(2 points)
(
,
)

Answer 1

I don't see the expressions for f(x) and g(x) in your message, so I can't tell which one has a y‑intercept. To decide which does, evaluate each at x = 0 — if 0 is in the function's domain, that function has a y‑intercept.

For the second part: solving y = −3(x−5)^2 + 7 for x gives the inverse(s)
x = 5 ± sqrt((7 − y)/3).
If we take the branch that is a square‑root function (the inverse of the right branch x ≥ 5), the inverse is
f⁻¹(x) = 5 + sqrt((7 − x)/3),
with domain x ≤ 7. Its minimum occurs at x = 7, giving y = 5.

So the minimum point is (7, 5).