Question

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

$\bf x = -\frac{6}{2×1}$

$\bf x = -\frac{6}{2}$

$\bf x = -3$

- 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! :)