Precalculus Polynomial, Power, and Rational Function Test

Question 1

Input and Output Values

f(-7)=8 and f(-4)=2

Answer 1

y1 = 8
y2 = 2
x1 = -7
x2 = -4

Question 2

Slope

Answer 2

a = y2-y1/x2-x1

Question 3

Linear function formula

Answer 3

y = a(x)+b

Question 4

Vertex form

Answer 4

a(x-h)^2+k

Question 5

Strong correlation

Answer 5

Points are stuck together

Question 6

Weak correlation

Answer 6

Points are spread out

Question 7

If the degree n is even, then

Answer 7

The ends go off in opposite directions

Question 8

If the degree n is odd, then

Answer 8

The ends go off in the same directions

Question 9

If the leading coefficient is positive, then

Answer 9

The right end of the graph is up

Question 10

If the leading coefficient is negative, then

Answer 10

The right end of the graph is down

Question 11

True or false x(3x-2)(x-4) x=0

Answer 11

True

Question 12

Finding regression

Answer 12

STAT. EDIT, [ENTER DATA], STAT, CALC, [TYPE], ENTER

Question 13

Fraction form

Answer 13

(Quotient) + (Remainder/Divisor)

Question 14

Polynomial form

Answer 14

f(x) = Divisor (Quotient) + Remainder

Question 15

Upper bound

Answer 15

Use synthetic division to see if nonnegative

Question 16

Lower bound

Answer 16

Use synthetic division to see if alternating negatives

Question 17

Writing a polynomial in standard form with irrational zeros

Answer 17

Add (x-(negative irrational zero) and (x-(positive irrational zero))

Question 18

Odd multiplicity

Answer 18

Crosses the x-axis

Question 19

Even multiplicity

Answer 19

Tangent to the x-axis

Question 20

You will never end up with “xi” because it always cancels out

Answer 20

True

Question 21

Linear factorization

Answer 21

All are possible factors of an answer is factored completely

Question 22

Given a zero, find the other zeros

Answer 22

Multiply the irrational zeros with (x-(negative irrational zero)) and (x-(positive irrational zero), complete long division, factor the quotient, find zeros of the factored pairs

Question 23

Reflection of the x-axis

Answer 23

y = −f(x)

Question 24

Reflection of the y-axis

Answer 24

y = f(−x)

Question 25

Vertical stretch

Answer 25

a f(x) when a > 1

If a should be negative, then the vertical compression or stretching is followed by a reflection across the x-axis

Question 26

Vertical shrink

Answer 26

a f(x) when 0 < a < 1

If a should be negative, then the vertical compression or stretching is followed by a reflection across the x-axis

Question 27

Horizontal stretch

Answer 27

f (ax) when 0 < a < 1

If a should be negative, the horizontal compression or stretching is followed by a reflection of the graph across the y-axis

Question 28

Horizontal shrink

Answer 28

f (ax) when if a > 1

If a should be negative, the horizontal compression or stretching is followed by a reflection of the graph across the y-axis

Question 29

Vertical asymptote

Answer 29

Set denominator to 0

Question 30

Horizontal asymptote

Answer 30

Degree numerator < degree denominator = y=0
Degree numerator = degree denominator = L.C.
Degree numerator > degree denominator = no HA

Question 31

Slant asymptote

Answer 31

Long division

Question 32

Domain

Answer 32

Associates with x-axis

Question 33

Range

Answer 33

Associates with y-axis

Question 34

A polynomial function with an odd degree and real coefficients has to have at least one real zero because imaginary roots come in conjugate pairs

Answer 34

True

Question 35

Finding x-intercepts

Answer 35

Zeros of numerator

Question 36

Finding y-intercepts

Answer 36

Set f(0)