Question

What are the domain and range of this function? y= (x+3)² - 5

A. Domain: [-5, ∞)
Range: [-∞,∞)

B. Domain: (-∞.∞)
Range: (-∞,∞)

C. Domain:(-∞,∞)
Range:[-5,∞)

D. Domain: (-5,∞)
Range: (-5,∞)

Answer 1

Hello!

`\bf y = ( x + 3 )^(2) - 5`

- Separate the function into parts to determine the domain of each part.

`\bf ( x + 3 )^(2) \\ x + 3 \\ 5`

- The domain of a polynomial function is the set of all real numbers.

`\bf x ∈ ℝ`

Domain: ( -∞; ∞ )

`\bf y = ( x + 3 )^(2) - 5`

- Write the second degree function in standard form.

`\bf y = x^(2) + 6x + 4`

- Identifies the coefficients a and b of the second degree function.

`\bf a = 1, b = 6`

- Find the x coordinate of the vertex by substituting a = 1 and b = 6 in x = -b / 2a.

`\bf x = -(6)/(2×1)`

`\bf x = -(6)/(2)`

`\bf x = -3`

- Calculates the value of the function for x = -3.

`\bf y = ( x + 3 )^(2) - 5`

`\bf y = -5`

Range: ( -3; -5 )

Answer: No answer

Good luck! :)