91Ó°ÊÓ

Use a graphing calculator to graph the function and its parent function. Then describe the transformations. \(f(x)=-(x+3)^2+\frac{1}{4}\)

Use a graphing calculator to graph the function and its parent function. Then describe the transformations. \(g(x)=-|x-1|-\frac{1}{2}\)

MAKING AN ARGUMENT Your friend claims that when writing a function whose graph represents a combination of transformations, the order is not important. Is your friend correct? Justify your answer.

Consider the system of linear equations below. Choose nonzero values for \(a, b\), and \(c\) so the system satisfies the given condition. Explain your reasoning. $$ \begin{aligned} &x+y+z=2 \\ &a x+b y+c z=10 \\ &x-2 y+z=4 \end{aligned} $$ a. The system has no solution. b. The system has exactly one solution. c. The system has infinitely many solutions.

A linear system in three variables has no solution. Your friend concludes that it is not possible for two of the three equations to have any points in common. Is your friend correct? Explain your reasoning.

In Exercises 39-44, identify the function family and describe the domain and range. Use a graphing calculator to verify your answer. \(g(x)=|x+2|-1\)

A florist must make 5 identical bridesmaid bouquets for a wedding. The budget is \(\$ 160\), and each bouquet must have 12 flowers. Roses cost \(\$ 2.50\) each, lilies cost \(\$ 4\) each, and irises cost \(\$ 2\) each. The florist wants twice as many roses as the other two types of flowers combined. a. Write a system of equations to represent this situation, assuming the florist plans to use the maximum budget. b. Solve the system to find how many of each type of flower should be in each bouquet. c. Suppose there is no limitation on the total cost of the bouquets. Does the problem still have exactly one solution? If so, find the solution. If not, give three possible solutions.

Identify the function family and describe the domain and range. Use a graphing calculator to verify your answer. \(h(x)=|x-3|+2\)

ABSTRACT REASONING The functions \(f(x)=m x+b\) and \(g(x)=m x+c\) represent two parallel lines. a. Write an expression for the vertical translation of the graph of \(f\) to the graph of \(g\). b. Use the definition of slope to write an expression for the horizontal translation of the graph of \(f\) to the graph of \(g\).

HOW DO YOU SEE IT? Consider the graph of \(f(x)=m x+b\). Describe the effect each transformation has on the slope of the line and the intercepts of the graph. a. Reflect the graph of \(f\) in the \(y\)-axis. b. Shrink the graph of \(f\) vertically by a factor of \(\frac{1}{3}\). c. Stretch the graph of \(f\) horizontally by a factor of 2 .