Question

function shown below.

\\f(x) = -\frac{3}{4}(-x)^2 + 8\\

a) choose the correct parent function.

• \\(y = x^2\\)
• \\(y = x^3\\)
• \\(y = |x|\\)
• \\(y = \sqrt{x}\\)
• \\(y = \sqrt3{x}\\)

b) choose the correct transformation (reflections).
reflection across both axes

c) choose the correct transformation (stretches/compressions).
vertical compression by a factor of 3/4

d) choose the correct transformation (vertical shifts).
select an answer

e) choose the correct transformation (horizontal shifts).

Explanation:

Step1: Identify parent function

$$y = x^2$$

Step2: Determine reflections

$$\text{Negative signs outside and inside indicate reflection across both axes.}$$

Step3: Determine stretches/compressions

$$\text{The factor } \frac{3}{4} \text{ outside indicates vertical compression by } \frac{3}{4}.$$

Step4: Determine vertical shift

$$\text{The term } +8 \text{ indicates a shift up by 8 units.}$$

Step5: Determine horizontal shift

$$\text{There is no constant added or subtracted inside the parentheses.}$$

Answer:

a) \(y = x^2\)
b) Reflection across both axes
c) Vertical compression by a factor of 3/4
d) Shift up by 8 units
e) No horizontal shift