Question

give the equation of the function g whose graph is described. 29) the graph of f(x) = \sqrt3{x} is shifted 7.6 units to the left. this graph is then vertically stretched by a factor of 4.7. finally, the graph is reflected across the x - axis.

Explanation:

Step1: Horizontal Shift Left

To shift the graph of \( f(x)=\sqrt[3]{x} \) 7.6 units to the left, we replace \( x \) with \( x + 7.6 \) in the function. So we get \( f(x + 7.6)=\sqrt[3]{x + 7.6} \).

Step2: Vertical Stretch

To vertically stretch the graph by a factor of 4.7, we multiply the function by 4.7. So the function becomes \( 4.7\sqrt[3]{x + 7.6} \).

Step3: Reflection across x - axis

To reflect the graph across the \( x \)-axis, we multiply the function by - 1. So the final function \( g(x) \) is \( g(x)=- 4.7\sqrt[3]{x + 7.6} \).

Answer:

\( g(x)=-4.7\sqrt[3]{x + 7.6} \)