# Randy - Functions

## 28 terms · Functions

### Domain

Possible input values. X.

### Range

Possible output values. Y.

f(x) = f(-x)

f(x) = -f(x)

### One-to-one Functions

Every output happens exactly once.

### Difference Quotient

[f(x+h) - f(x)] / h

### Inverse Functions

Swap x and y then solve.

### One-to-One Functions (Graph)

Each horizontal line crosses the line exactly once.

### Onto Function (Graph)

Each horizontal line crosses the line at least once.

### Onto Function

The function hits all possible y's.

x = [-b] / [2a]

### Parabola opens up

When A is positive

### Parabola opens down

When A is negative

### Parabola y-Intercept

Let all x's equal 0.

### Parabola x-intercept

Set equation equal to 0 then factor.

### Shirt Graph Right

Replace x with (x - a). Where a is constant.

### Shift Graph Left

Replace x with (x + a). Where a is constant.

### Shift Graph Up Vertically

Add a to f(x). (ie f(x) +3). Where a is constant.

### Shift Graph Down Vertically

Subtract a from f(x). (ie f(x) -3). Where a is constant.

### Flip over X-Axis

Replace f(x) with -f(x).

### Flip over Y-Axis

Replace f(x) with f(-x)

### Compress Graph Horizontally

Multiply x by constant a. (ie f(ax)). Where a is a cosntant.

### Stretch Graph Horizontally

Multiply x by constant 1/a. (ie f((1/a)x)). Where a is a cosntant.

### Compress Graph Vertically

Multiply f(x) by constant 1/a. (ie (1/a)f(x)). Where a is a constant

### Stretch Graph Vertically

Multiply f(x) by constant a. (ie (a)f(x)). Where a is a cosntant.

### Horizontal Asymptotes

None: Highest power is in numerator.
y=0: Highest power in in denominator only.
Fraction: Both numerator and denominator have same highest power.

### Vertical Asymptotes

Where denominator is equal to 0.

### Oblique Asymptotes

Numerator is a power 1 higher then the denominator.

Divide equations. Ignore remainder.