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vocabulary

100

The set of all output values for a function or relationship.

range

200

A function that “undoes” what the original function does.

inverse function

300

The conversion of a function to a corresponding function, often by a factor of constant k.

transformation (of a function)

400

Inverse exponential functions.

logarithmic functions

500

In this course, a line that a graph of a curve approaches but never meets. represented as dashed lines.

asymptote

how can i undo a function?

100

Solve the following equations, if possible. Some you can solve exactly, others approximately. If a solution is not possible, explain how you know.

1^x=5

not possible

200

Tasha only has $3 saved but has a goal of doubling the total amount of money she has saved every month.

Write an equation for the total amount of money Tasha has saved after x months.

t(x)=3*2^x

300

Graph the inequalities y(>or =)|x-2|and 

y(< or = 4-|x|).

What is the area of the enclosed region?

A=6

shaded area is above in a V

and below (look at homework answers)

400

If the cost of a movie ticket now averages $11.50, interpret the meaning of the expression 11.50(1.083)^t

movie tickets cost 11.50 and go up by 8.3% regularly

How can I determine an inverse?

100

Graph 1 draw line of symmetry graph inverse

shown on board

200

graph 2 show line of symmetry and show its inverse

graph on board

300

graph 3 whats its inverse draw line of symmetry

graph on board

400

f(x)=3x-8 graph show inverse.

x+8/3

What can I do with inverses?

100

Trejo says that if you know the x‑intercepts, y‑intercepts, domain, and range of a function then you automatically know the x‑intercepts, y‑intercepts, domain, and range of its inverse. Hilary disagrees. She says you know the intercepts but that is all you know for sure. Who is correct? Justify your answer

Trejo is correct as long as the domains are restricted properly

200

To what power do you have to raise:

3 to get 27?

5 to get 625?

81 to get 3

3, 4, 1/4

300

Kirsta was working with the function machine shown at right, but when she turned her back, her little brother Caleb dropped in a number. She did not see what he dropped in, but she did see what fell out: 9

1. What operations must she perform on 9 to undo what her machine did? Use this to determine what number Caleb dropped in.

k(x)=sqaureroot x+5

sqaure it 

subtract 5

81-5= 76

400

1. Write an equation for a machine that will undo Kirsta’s machine.

k(x)=sqaureroot x-5

x²-5

How can I undo an exponential function?

100

Using the idea behind the Ancient Puzzle you studied today, what is the value of  in each equation below? Explain your reasoning.

log_b(243)=5

log_d(0.001)=-3

b=3

d=10

200

exponential form

7^y=x

whats the log form?

y=log₇(x)

300

exponential form 

A^k=C

find log form

k=log_A(C)

400

log form

log_1/2(K)=N

what is exponential form?

log_1/2(k)=N