Chapter 6.1

Question 1

Vertical Shift

Answer 1

adding or subtracting a constant to or from the function’s output (outside change)

Question 2

adding a constant (vertical shift) makes the graph go…

Answer 2

up

Question 3

subtracting a constant (vertical shift) makes the graph go…

Answer 3

down

Question 4

Horizontal shift

Answer 4

adding or subtracting to or from the function’s input (inside change)

Question 5

g(x)=f(x-1) means the graph moves…

Answer 5

to the right 1

Question 6

p(x)=f(x+3) means the graph moves…

Answer 6

to the left 3

Question 7

Why do horizontal shifts move opposite of what you think?

Answer 7

because the translation of f(x) can be expressed as y= f(x-h)+K where h is already being subtracted

Question 8

j(x)= -f(x) is a reflection across the…

Answer 8

x-axis (outside change)

Question 9

k(x)= f(-x) is a reflections across the…

Answer 9

y-axis (inside change)

Question 10

Asymptote

Answer 10

line/curve that a graph approaches, but never touches

Question 11

Symmetry

Answer 11

graphs that don’t change when reflected

Question 12

Even Function

Answer 12

symmetric about the y-axis, power functions with even exponents

Question 13

Odd Functions

Answer 13

reflected across the x and y-axis, symmetric about the origin

Question 14

How do you algebraically know that a function is even?

Answer 14

if f(-x)=f(x)

Question 15

How do you algebraically know that a function is odd?

Answer 15

if (f-x)= -f(x)

Question 16

How do you algebraically know that a function is neither even nor odd?

Answer 16

check that f(1) does not equal f(-1)