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21 Cards in this Set

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  • Back
What is:
{2,3,4,5}U{2,4,6,8}?
Answer: {2,4}
Union means that the numbers (or points) in the resulting set must be in both initial sets.
What is:
{2,3,4,5}∩{2,4,6,8}?
Answer: {2,3,4,5,6,8}
Intersection contains every number (or point) that exists in both initial sets.
y = 5x + 8

Find the slope and intercept.
Answer: Intercept (y) = 8. Slope = 5/1.
Factor:

2^4 + 36
Answer: (2^2 + 6)(2^2 - 6)
Factor:
x^2 + 5x + 6
Answer: (x + 2)(x + 3)
Tricky:
You have a parabola, and you need to factor out the x coordinates from...
x^2 + 5x + 10
Step 1: x^2 + 5x + 6 + 4
Step 2: (x+2)(x+3) + 4

Note: Now you have your 2 x-coordinates and your y-coordinate.
Simplify:

-12h > -6xh
Answer: 2 < x

Divide both sides by -6h and reverse the sign because you have divided by a negative number.
What kind of graph, and what direction is it going?

y = -x^2 + 3x + 8
Parabola that opens downward.
What kind of graph, and what direction is it going?

x = -y^2 + 3y + 8
Parabola that opens to the left.
Not a function.
What kind of graph, and what direction is it going?

y = (x-4)^ + 8
Parabola that opens upward.
Which arithmetic of functions has a catch?
Division.
You need to find the domain of function in the denominator before simplifying or the correct domain will most likely be masked or altered.
Is a mountain concave up or concave down?
Concave down, because it is opening downwards from the top point.
Is a puddle concave up or concave down?
Concave up, because it is opening upwards from the bottom point.
What is happening to this function?
f(x + k)
Shift left k spaces.
What is happening to this function?
f(x) + k
Shift up k spaces.
What is happening to this function?
-f(x - k)
Shift right k spaces.
Then the entire graph is inverted because of the negative.
What is happening to this function?
f(x) - k
Shift down k spaces.
What is happening to this function?
(1/2)*f(x)
all y values are halved.
What is happening to this function?
f( (1/2)*x )
all x values are doubled.
What is happening to this function?
-f(2x)
all x values are halved.
Then the entire graph is inverted because of the negative.
What is happening to this function?
2f(x)
All y values are doubled.