Identify the parent function from the function rule. Describe the transformation of the parent function that given function represents. Use your graphing calculator to check your answers.

g(x)=3 x

Linear function f is transformed to produce g. Write g(x) in terms of f(x).

f(x)=x-7 is reflected across the x-axis.

Harry is working on a budget for a concert. The given graph shows the total cost of renting the hall. A cleaning fee of 40 dollars for each rental is included in the graph. Use the graph for given exercise.

What is the cost of renting the hall for 2 hours? for 3 hours? for 6 hours? for 7 hours?

The table lists the median age of males living in the United States based on the results of the U.S. Census over the past few decades.

a. Let t represent time (in years since 1970 ), and let $a_M$ represent the median age of males. Make a table of paired values of t and $a_{M^{-}}$Then draw a scatter plot.

b. Draw a line of fit on the scatter plot and find an equation of the line.

c. Calculate the residuals, and make a residual plot. t-values

d. Evaluate the suitability of a linear fit and the goodness of the fit.

e. Predict the median age of males in 1995 and 2015. Identify each prediction as an interpolation or an extrapolation, and then compare the predictions with these median ages of males from the Census Bureau: 33.2 in 1995 and an estimated 35.9 in 2015.

Linear function f is transformed to produce g. Write g(x) in terms of f(x).

f(x)=3 x is translated 6 units up.

Perform the given translation on the point (5,-3) and give the coordinates of the translated point.

6 units right

The given graph shows a translation of the function f(x)=x.

a. Describe the translation in two different ways.

b. Explain why the translations are the same.

c. Other parent functions do not have this same feature. Use the parent function $y=x^2$ to explain why.

The students in Ms. Hari's English class are planning to print a booklet of their creative writings. Use the table of publishing prices.

The students decide to print a booklet containing black and white text only. Write a function, $C(\rho)$, to show the cost of printing a booklet of p pages with a cover that also has text only.

Katy and Peter are writing a paper about the history and use of cell phones. They make a graph of the data in the table. They want to determine the parent function for the graph.

Peter wants to compare the graph to the function f(x)=7 x+2. How would the graph of f(x)=7 x+2 compare to its parent function f(x)=x ?

Vern created a website about his school's sports teams. He has a hit counter on his site that lets him know how many people have visited the site. The table shows the number of hits the site received each day for the first two weeks. Make a scatter plot for the data using the day as the independent variable. Sketch a line of best fit and find its equation.

As a science project, Shelley is studying the relationship of car mileage (miles per gallon) and speed (miles per hour). The table shows the data Shelley gathered using her family's hybrid vehicle.

Make a scatter plot of the data. Identify the correlation.

Identify the parent function for h from its function rule. Then graph h on your calculator and describe what transformation of the parent function it represents.

$$h(x)=\sqrt{x+4}$$

The point (-2,7) is translated 3 units right and 2 units down. What are the coordinates of the translated point?

A. (0,4)

B. (1,5)

C. (-5,5)

D. (1,9)

Perform the given translation on the point (2,5) and give the coordinates of the translated point.

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