91Ó°ÊÓ

REASONING The graph of \(g(x)=-4|x|+2\) is a reflection in the \(x\)-axis, vertical stretch by a factor of 4 , and a translation 2 units down of the graph of its parent function. Choose the correct order for the transformations of the graph of the parent function to obtain the graph of \(g\). Explain your reasoning.

Identify the function family and describe the domain and range. Use a graphing calculator to verify your answer. \(f(x)=5 x^2-2\)

THOUGHT PROVOKING You are planning a cross-country bicycle trip of 4320 miles. Your distance \(d\) (in miles) from the halfway point can be modeled by \(d=72|x-30|\), where \(x\) is the time (in days) and \(x=0\) represents June 1 . Your plans are altered so that the model is now a right shift of the original model. Give an example of how this can happen. Sketch both the original model and the shifted model.

In the same coordinate plane, sketch the graph of the parent quadratic function and the graph of a quadratic function that has no \(x\)-intercepts. Describe the transformation(s) of the parent function.

Graph the functions \(f(x)=|x-4|\) and \(g(x)=|x|-4\). Are they equivalent? Explain.

Your friend says two different translations of the graph of the parent linear function can result in the graph of \(f(x)=x-2\). Is your friend correct? Explain.

A person swims at a constant speed of 1 meter per second. What type of function can be used to model the distance the swimmer travels? If the person has a 10-meter head start, what type of transformation does this represent? Explain.

You are playing basketball with your friends. The height (in feet) of the ball above the ground \(t\) seconds after a shot is made is modeled by the function \(f(t)=-16 t^2+32 t+5.2\). a. Without graphing, identify the type of function that models the height of the basketball. b. What is the value of \(t\) when the ball is released from your hand? Explain your reasoning. c. How many feet above the ground is the ball when it is released from your hand? Explain.

Compare each function with its parent function. State whether it contains a horizontal translation, vertical translation, both, or neither. Explain your reasoning. a. \(f(x)=2|x|-3\) b. \(f(x)=(x-8)^2\) c. \(f(x)=|x+2|+4\) d. \(f(x)=4 x^2\)

Determine whether the ordered pair is a solution of the equation. \(f(x)=|x|-3 ;(-2,-5)\)