Question

Which of the following represents the range of the function g(x) = -3(x+5)^2+10 1. y > 102. y > -153. y <= 104. y<=15

Answer 1

3. y ≤ 10

Explanation:

Given the function:

`g\mleft(x\mright)=-3\left(x+5\right)^2+10`

We want to find the range.

The range of a function is the set of all the values of y for which a function is defined.

Compare g(x) with the vertex form of a quadratic function given below:

`y=a(x-h)^2+k`

• The vertex of g(x) = (-5, 10)

Since the value of a is -3 (negative), the parabola opens down and thus, the vertex is a maximum.

• The y-value at the vertex = 10

Thus, the range of g(x) is:

`y\leq10`

Option 3 is correct.