Graphs
Functions
Polynomials
Solving
Formula Sheet
100
(Section 4.1)
Find the domain and range of the graphed relation:
Find the domain and range of the graphed relation:
Domain: (-∞, ∞)
Range: [-3, ∞)
Range: [-3, ∞)
100
(Section 4.3)
f(4) = 9
100
(Section 2.3)
Solve
(x-3)2 = 39 using the Square-Root Property.
Solve
(x-3)2 = 39 using the Square-Root Property.
x = 3 ± √39
100
(Section 2.6)
Solve
√(25x2 + 12x +17)
= 5x + 3
Solve
√(25x2 + 12x +17)
= 5x + 3
x = -4⁄9
100
(Section 4.2)
Determine the vertex of the parabola given by the function
f(x) = 3x2 - 6x + 1
Determine the vertex of the parabola given by the function
f(x) = 3x2 - 6x + 1
(1, -2)
200
(Section 3.2)
Find the x- and y-intercepts of
-3x + 2y = 12. Graph the line.
Find the x- and y-intercepts of
-3x + 2y = 12. Graph the line.
200
(Section 4.5)
Given f(x) = |x+4| and
g(x) = x²
Find (g-f)(-5)
Given f(x) = |x+4| and
g(x) = x²
Find (g-f)(-5)
(g-f)(-5) = 24
200
(Section 5.2)
Use synthetic division to determine if the given value for k is a zero of this polynomial and find the value of p(k).
p(x) = 2x4 - 7x3 + 11x - 26
k = 3
Use synthetic division to determine if the given value for k is a zero of this polynomial and find the value of p(k).
p(x) = 2x4 - 7x3 + 11x - 26
k = 3
No, p(k) = -20
200
(Section 2.1)
Solve |8x + 5| = 3
Solve |8x + 5| = 3
x = -1, -¼
200
(Section 3.3)
Find the equation of the line passing through the points (2, 0) and (-7, 6)
Find the equation of the line passing through the points (2, 0) and (-7, 6)
y = -2⁄3 x + 4⁄3
300
(Section 4.4)
For f(x)= -2 - |x + 1|
Indicate how the more basic function has been shifted, reflected, stretched, or compressed.
For f(x)= -2 - |x + 1|
Indicate how the more basic function has been shifted, reflected, stretched, or compressed.
Horizontal Shift: Left 1 unit
x-Axis Reflection
Vertical Shift: Down 2 units
x-Axis Reflection
Vertical Shift: Down 2 units
300
(Section 4.6)
Find the inverse of
T(x) = (x-2)3 if possible.
Find the inverse of
T(x) = (x-2)3 if possible.
T-1(x) = ∛(x) + 2
300
(Section 7.5)
Solve
log(x-7) + log(x+2) = 1
Solve
log(x-7) + log(x+2) = 1
x=8
300
(Section 2.5)
Solve
x⁄x+1 + 2-x⁄x-8
= 1⁄x²-7x-8
Solve
x⁄x+1 + 2-x⁄x-8
= 1⁄x²-7x-8
x = 1⁄7
300
(Section 7.5)
Find the amount of time it would take $200 to double in an account earning 7%, compounded continuously.
Find the amount of time it would take $200 to double in an account earning 7%, compounded continuously.
9.9 years
400
(Section 5.1)
Find the x- and y-intercepts of
g(x)=(2x+3)(x-2)2
Graph the polynomial.
Find the x- and y-intercepts of
g(x)=(2x+3)(x-2)2
Graph the polynomial.
400
(Section 4.2)
The profit from selling s thousand items is given by the function
P(s) = 8300s - 240,000 - 10s2 Find the value of s that gives the maximum profits.
The profit from selling s thousand items is given by the function
P(s) = 8300s - 240,000 - 10s2 Find the value of s that gives the maximum profits.
s = 415
400
(Section 5.2)
Construct a degree 3 polynomial with the zeros
-1, 4, 5 with a leading coefficient of 2.
Construct a degree 3 polynomial with the zeros
-1, 4, 5 with a leading coefficient of 2.
p(x) = -2x3 + 16x2 + 38x - 40
400
(Section 7.1)
Solve 45-2x = 32x
Solve 45-2x = 32x
x = 10⁄9
400
(Section 3.6)
Find the equation of a circle with a center of (0, -3) and passing through the point (-5, 1)
Find the equation of a circle with a center of (0, -3) and passing through the point (-5, 1)
x2 + (y + 3)2 = 41
500
(Section 6.1a)
Find the vertical and horizontal asymptotes of
r(x) = -2x⁄x²-1
Graph the rational function.
Find the vertical and horizontal asymptotes of
r(x) = -2x⁄x²-1
Graph the rational function.
VAs: x=-1, x=1
HA:y=0
HA:y=0
500
(Section 4.5)
Given p(x) = x - 9 and
q(x) = |x|, find
(p ∘ q)(x)
Given p(x) = x - 9 and
q(x) = |x|, find
(p ∘ q)(x)
(p ∘ q)(x) = |x| - 9
500
(Section 5.4)
Given that 3i is a zero, factor completely:
P(x) = x4 - 3x3 + 11x2
- 27x + 18
Given that 3i is a zero, factor completely:
P(x) = x4 - 3x3 + 11x2
- 27x + 18
P(x) =
(x - 3i)(x + 3i)(x - 2)(x - 1)
(x - 3i)(x + 3i)(x - 2)(x - 1)
500
(Section 2.2)
Solve |2x + 7| > 3
Give the solution in interval notation.
Solve |2x + 7| > 3
Give the solution in interval notation.
(-∞, -5)U(-2, ∞)
500
(Section 2.3)
Use the quadratic formula to solve:
4x = 13 + x2
Use the quadratic formula to solve:
4x = 13 + x2
2 ± 3i