What is the range of the function f(x) = −(x + 3)2 + 7?

Question

15-08-2019
Mathematics

contestada

What is the range of the function f(x) = −(x + 3)2 + 7?

Respuesta :

Otras preguntas

In the step by step simplification of expression below which property is not used? 3(1+x)3(x+1)3(x)+3(1)3x +3 A) associative B) commutative C) distributive D)

A laptop computer is priced at $650. If the sales tax is 5%, find the total cost of the computer, including sales tax.

In the step by step simplification of expression below which property is not used? 3(1+x)3(x+1)3(x)+3(1)3x +3 A) associative B) commutative C) distributive D)

You have a piece of wood that is 7 3/4 feet long. You want to cut one piece that is 3 7/12 feet long and one piece that is 4 1/12 feet long. Do you have enou

In the step by step simplification of expression below which property is not used? 3(1+x)3(x+1)3(x)+3(1)3x +3 A) associative B) commutative C) distributive D)

You have a piece of wood that is 7 3/4 feet long. You want to cut one piece that is 3 7/12 feet long and one piece that is 4 1/12 feet long. Do you have enou

19allenethm 19allenethm · Answer 1 · 2019-08-15T07:53:09+02:00

19allenethm 19allenethm

15-08-2019

Answer:

(-∞,7]

Step-by-step explanation:

This parabola is negative. This means that the vertex will be the highest possible y value. The vertex of this parabola is at (-3,7). This means that the range would be (-∞,7]

Answer Link

tramserran tramserran · Answer 2 · 2019-08-16T09:16:56+02:00

Answer: y ≤ 7

Interval notation is: (-∞, 7]

Step-by-step explanation:

First, remember that range represents the y-values of the function.

-(x + 3)² + 7 is in vertex form: a(x - h)² + k where

(h, k) is the vertex
a is negative so it is reflected across the x-axis (upside-down parabola)

Therefore, the parabola has a maximum y-value at k (which is 7) and continues downward to negative infinity. ⇒ Range: y ≤ 7