Final Exam

Question 1

How do you add/subtract radicals?

Answer 1

Simplify the radicals and then add the simplified radicals.

Question 2

How do you multiply radicals?

Answer 2

Multiply the coefficients, and multiply the radicals separately. Treat the radicals like algebra unknowns, using foil.

Question 3

What is a relation?

Answer 3

a rule that gives one or more outputs for every valid input.

Question 4

What is a function?

Answer 4

A rule that gives exactly one output for every input.

Question 5

What does f(x) mean?

Answer 5

Apply the function “f” to the variable “x”

Question 6

What’s the domain?

Answer 6

Every possible x value or input

Question 7

Whats the range?

Answer 7

Every possible y value or output

Question 8

What’s a linear function?

Answer 8

A function thats a straight line made by multiplying x

Question 9

Whats a quadratic function?

Answer 9

A function thats a parabola made by x^2

Question 10

Whats a reciprocal Function?

Answer 10

A function made by the reciprocal of x, 1/x. Undefined at x = 0

Question 11

What’s a square root function?

Answer 11

a function made from the square root of x

Question 12

What’s an absolute value function

Answer 12

a v-shaped function thats |x|

Question 13

Whats an exponential function?

Answer 13

A function that is made by x^b, bends before 0

Question 14

Whats the inverse of a function?

Answer 14

The inverse of a function is a relation which reverses or undergoes the operations performed by the function.

Question 15

How do you find the inverse of a function

Answer 15

replace f(x) with y
interchange x and y
solve for y
replace y with inverse of f(x)

Question 16

True or false: inverse of f(x) equals 1/f(x)

Answer 16

False.

Question 17

What are the domain and range of the inverse of f(x)?

Answer 17

The domain of the inverse function is the same as the range of the original function. The range of the inverse function is the same as the domain of the original function.

Question 18

What’s the graph of the inverse of f(x)?

Answer 18

The graph of f(x) reflected on the diagonal line where x = y

Question 19

What’s the slop of the inverse of f(x)

Answer 19

the reciprocal of the slope of f(x) (a slope of 3/4 becomes 4/3, 5 becomes 1/5)

Question 20

What are the intercepts of the inverse of f(x)

Answer 20

The inverse’s x-intercepts are the same as the originals y-intercepts and vica-versa

Question 21

How do you create the inverse of a graph?

Answer 21

draw a line where x = y
find the x-interecepts, y-intercepts, and diagonal line intercepts
draw the new graph so it meets all the same places

Question 22

in y = af(k(x-d)) + c, what does c do?

Answer 22

Slides the graph virtically

Question 23

In y = af(k(x-d)) + c what does d do?

Answer 23

Slides it horizontally - remember that d is subtracted, not added.

Question 24

In y = af(k(x-d)) + c what does a do?

Answer 24

Stretches if vertically.

Question 25

In y = af(k(x-d)) + c what does k do?

Answer 25

Compresses it vertically. The graph will be stretched if 0 < k < 1

Question 26

How do you flip the graph of y = af(k(x-d)) + c over the x axis?

Answer 26

Make a equal to -1

Question 27

How do you flip y = af(k(x-d)) + c over the y axis

Answer 27

Make k equal to -1

Question 28

What transformation happens to y = f(x) + 2

Answer 28

Translation Two Units up

Question 29

What transformation happens to 1/2 f(x)

Answer 29

Compressed vertically by a factor of 2

Question 30

What transformation happens to f(x+2)

Answer 30

translation two units to the left

Question 31

What transformation happens to y = f(2x)

Answer 31

Compressed horizontally by a factor of two

Question 32

True or false: a should be applied before c

Answer 32

true

Question 33

true or false: d should be applied before k

Answer 33

false

Question 34

Whats the general form of a quadratic equation?

Answer 34

y = ax^2 + bx + c

Question 35

Whats the standard or vertex form of a a quadratic equation?

Answer 35

y = a(x - h)^2 + k

Question 36

how do you find the the vertex of a parabola?

Answer 36

In the equation a(x - h)^2 + k, [h, k] is the vertex

Question 37

How do you complete the square?

Answer 37

``` ax^2 + bx +c factor out a a(x^2 + b/ax) + c divide b/2 by 2 and square it a(x^2 + b/ax + (b/2a)^2 - (b/2a)^2) + c ```