Linear Equations
−8 + 4
-4
Determine the following. Write all answers in interval notation.
{(3, −5), (0, −3), (3,1)}
Domain:
Range: Function? Yes? or No?
Domain: (3, 0)
Range: {−5, −3, 1}
Distribute the following. Simplify your answers.
3x(x + 2)
3x^2+6x
Simplify the following expressions.
√27
3√3
Simplify the following expressions.
8 2/3
26/3
3 − 3 × 6 + 2
-13
Evaluate the following given the functions:
g(x) = x^2 + 1
g (−2)
5
Factor the following.
x^2 + x − 2
(x+2)(x−1)
x = -2 x = 1
Simplify the following expressions.
x^4 x^5/x^2
x9/x2
x^9−2=x^7
Draw the graph that represents the store: Professor Ottino was walking to his bus stop until he realizes he forgot his wallet. Professor Ottino needs his wallet to buy himself a Big Mac for lunch, so he jogs back home. Realizing he going to be late for the bus he runs to his bus stop.
Professor Ottino will determine the answer on his own.
Graph a relation below with the following.
Domain: (−∞, ∞)
Range: (−∞, 4)
Professor Ottino will determine the answer on his own.
Use the Quadratic Formula to find the following x-intercepts.
2x^2 − 3x − 9 = 0
x=3 and x=−3/2
Describe what it means when you need to find Intervals where f(x) is concave up and Intervals where f(x) is concave down.
Concave up: Graph bends upward like a smile → f(x) > 0
Concave down: Graph bends downward like a frown → f(x) < 0
How to find: Take the second derivative, check where it’s positive (up) or negative (down).
State whether the following are proportional, linear or exponential relationships. If they are proportional or linear, state the CROC (Constant Rate of Change). If they are exponential, state the Growth Factor.
y = 1/3∙ 2^x
Relationship: Exponential
Growth Factor: 2
Calculate the Rate of Change of the following. Simplify your answer. (12,−8) and (-6, 15).
m=−23/18
State all values in the domain of the following. Write all answers in interval notation.
h(x) = 1/x+5
(−∞,−5)∪(−5,∞)
Find the y-intercept, x-intercepts however you want.
y = x^2 + 2x
Y-intercept: (0,0)
X-intercepts: (0,0), (−2,0)
What are Critical Point(s) (Relative/Absolute) Max / Min of a graph
Critical points: where f'(x) = 0 or undefined.
Relative max/min: local peaks (max) or valleys (min).
Absolute max/min: the highest or lowest value on the whole graph.
Solve the following. Log Work!!!!
2 ^x+3 = 5
−0.678
Write an equation in Point Slope Form (y − y1 = m(x − x1)) and Slope Intercept Form (y = mx + b) given the following.
Points: (−7,20), (5,−16), (11,−34)
y−20=−3(x+7)
y=−3x−1
State all values in the domain of the following. Write all answers in interval notation.
i(x) = 2x−3/5
(−∞,∞)
Find the y-intercept, x-intercepts however you want.
y = 3x^2 − 5x − 2
Y-intercept: (0,−2)
X-intercepts: (2,0) and (-1/3, 0)
Find the following components of y = 3x^2 − 5x − 2
Domain (Interval Notation)
Range (Interval Notation)
Y-intercept: ????
X-intercepts: ???? (By whatever)
Domain: (−∞,∞)
Range: [−49/12,∞)
X-intercepts: (2,0), (−13,0)
Solve the following. Log Work!!!!
logx36 = 2
x=6