5-78.Ifx= 7Y, How Can You Rewrite This Equation Iny=Form? Explain

Name: ______Date: ______

HW IM3 5.2.3-5.2.4 Block: ____

5-78. If x = 7y, how can you rewrite this equation in y = form? Explain.

5-79. Krista was staring at the problem below with a confused look at on her face.

11 log66 = ?

“What’s the matter?” asked Jonique. “It seems like the answer should be easy but I keep going around in circles in my mind,” Krista replied. Jonique chuckled. “Yeah, it's just like asking ‘What is the name of the boy whose name is Bob?’” she laughed. Unfortunately, this did not help Krista at all. Can you help her? Explain to Krista what the expression above equals and why, and how it relates to Jonique’s question about Bob.

5-81. This problem is a checkpoint for transformations of functions. It will be referred to as Checkpoint 5.

Make a complete graph of each function below without using a graphing calculator. State the family of functions, and describe how each coefficient in the equation transforms the location or shape of the graph in relation to the parent function.

a) f(x) = + 4 b) h(x) = 3

Write an equation in graphing form for each equation below: c. d.

5-84. Given f(x) = –2x2 – 4 and g(x) = 5x + 3:

a. What is f(–7)? b. What is g(–2)? c. If f(x) = c, what is x?

d. If g(x) = c, what is x? e. Write an equation for g–1(x). 5-89. Copy these equations and solve for x. You should be able to do all these problems without a calculator.

a. logx(25) = 1 b. x = log3(9)

c. 3 = log7(x) d. log3(x) =

e. 3 = logx(27) f. log10(10000) = x

5-90. Sketch a graph of y = 3log(x + 4).

5-91. Is it true that log3(2) = log2(3)? Justify your answer.

5-94. If 24 = y, is it true that log(24) = log(y)? Justify your answer.

5-95. Let f(x) = and f –1(x) = –(x + 6)2 + 7. a. State the domains and ranges of f and f –1. If needed, restrict the domains so that they are inverses of each other.

b. Predict the output of f –1(f(a)). Then check your prediction algebraically. Show all your work.