H PreCalc - 1.3 to 1.4

f(x)=3x+1

Domain: ℝ

Range: ℝ

f(x)=|x+7|

Domain: ℝ

Range: ℝ ≥ 0

f(x)=√x-3

Domain: ℝ ≥ 3

Range: ℝ ≥ 0

f(x)= -3|x-2|

Domain: ℝ

Range: ℝ ≤ 0, multi[lied by negative must be negative

(-∞, + ∞)

Increasing

(-∞, -3), [-3, 3], (3, +∞)

Increasing, Constant, Decreasing

(-∞, -4), [-4, 4], (4, +∞)

Increasing, Decreasing, Increasing

Relative Minimum

The lowest dip in a piecewise linear approx.

Relative Maximum

The highest peak in a piecewise linear approx.

Even function

Graph is symmetric with respect to the y-axis. If (x,y) is a point on the graph, so is (x,y)

Odd function

Graph is symmetric with respect to the origin. If (x,y) is a point on the graph, so is (x,y), ex, (1,-7) and (-1, 7)

Not a function

Graph is symmetric with respect to the x-axis. If (x,y) is a point on the graph, so is (x,y)

A function is ____ if, for each x in the domain of ƒ, ƒ(x) = ƒ(x)

EVEN

A function is ____ if, for each x in the domain of ƒ, ƒ(x) = ƒ(-x)

ODD

Vertical Shift c units upward↑

h(x)=ƒ(x)+c

Vertical Shift c units downward↓

h(x)=ƒ(x)-c

Horizontal Shift c units to the right→

h(x)=ƒ(x-c)

Horizontal Shift c units to the left←

h(x)=ƒ(x+c)

Reflection in the x-axis

h(x)=ƒ(x)

Reflection in the y-axis

h(x)=-ƒ(x)

Vertical Stretch

y=cƒ(x) c > 1

Vertical Shrink

y=cƒ(x) 0 < c < 1

Horizontal Stretch

y=ƒ(cx) 0 < c < 1

Horizontal Shrink

y=ƒ(cx) c > 1

- Horizontal Stretch

- reflection across y

- _ to the left

y=√-½x-8

- Reflect on y

- _ left

ƒ(x)= |-x-4|

- _ right

- Reflect on y

ƒ(x)= |-x+4|