Question

write the function with the given transformation from the given parent function.
f(x) = \sqrt3{x}

• reflected across the x - axis
• vertically stretched by a factor of 5
• shifted up 7

f(x) = \square \sqrt3{\square} \square \square

Explanation:

Step1: Reflect over x-axis

Multiply parent function by -1: $-\sqrt[3]{x}$

Step2: Vertical stretch by 5

Multiply by stretch factor: $-5\sqrt[3]{x}$

Step3: Shift up 7

Add 7 to the function: $-5\sqrt[3]{x} + 7$

Answer:

$f(x) = -5\sqrt[3]{x} + 7$