Question

HelppppppFunction f is a(n)functionThe graph is a reflection in thewith a verticaland atranslationunits:The domain of f isThe domain of the parent function is;The range of f isThe range of the parent function is

Answer 1

In order of appearance of boxes

• quadratic

• x-axis

• stretch

• 3 (units)
• up
• all real numbers
• all real numbers
• y ≤ 3
• y ≥ 0

Explanation:

The given function f(x) = -2x² + 3 belongs to the quadratic family of equations. A quadratic equation has a degree of 2. The degree is the highest power of the x variable in the function f(x)

The parent f(x) = x²

Going step by step:

2x² ==> graph x² is vertically stretched by 2. For any value of x in x², the new y value is twice that the old value. For example, in the original parent function x², for x = 2, y = 4. In the transformed function 2x², for x = 2, y = 2 x 4 = 8 so it has been stretched vertically. It becomes skinnier compared to the original

-2x² => graph is reflected over the x-axis. It is the mirror image of the original graph when viewed from the x-axis perspective

-2x² + 3 ==> graph is shifted vertically up by 3 units

Domain is the set of all x-input values for which the function is defined. For both x² and -2x² + 3 there are no restrictions on the values of x. So the domain for both is the set of all real numbers usually indicated by
-∞ < x < ∞

The range is the set of all possible y values for a function y = f(x) for x values in domain.

The range of f(x) = x² is x≥ 0 since x² can never be negative

Range of -2x² + 3 is x ≤ 3 : Range of -2x² is y ≤ 0 since y cannot be negative and therefore range of -2x² + 3 is y ≤ 3