Practice with Quick Sketches

Last Class…O Vertical Line TestO Quick Sketches of 6 Important

Functions

Learning TargetsBy the end of class, students will be able to:O Quick sketch 6 common functionsO Use shifting to move graphs

ShiftingO Two Types of Shifts

O Vertical shifts: Up and downO Horizontal Shifts: Left and Right

Vertical ShiftsO A VERTICAL SHIFT is given by a +/-

constant next to the variable termO Examples:

O f(x) = x + 3Compared to our quick sketch of f(x) = x, the graph is shifted 3 units UP

Vertical ShiftsO Whether the shift is UP or DOWN

depends on the sign in front of the numberO Positive: Graph shifts UPO Negative: Graph shifts DOWN

Horizontal ShiftsO A HORIZONTAL SHIFT is given by a

+/- constant inside the parenthesis or radical sign

O Example: f(x) = (x – 3)2 Compared to the quick sketch of the function f(x) = x2, the sketch of our function is moved 3 units to the right.

Horizontal ShiftsO Whether the shift is LEFT or RIGHT

depends on the sign in front of the numberO Positive: Graph shifts LEFTO Negative: Graph shifts RIGHT

“Flipping”O When there is a NEGATIVE sign in

front of your function, that means that you turn the function upside down, or 90°

O Example: f(x) = -|x|Compared to the quick sketch of the function f(x) = |x|, the sketch of our function is turned upside down.

One person from each group needs to grab…1. A white board2. A marker3. An eraser

“Lightning” RoundO You will have 1 minute to sketch the

given graphO Point goes to the every group who

gets it rightO Group with the most points at the

end of the period gets a prize (candy)

f(x) = x2

f(x) = (x – 1)3

f(x) = -|x| - 2

f(x) = x + 5

f(x) = √x

f(x) = -x2 + 3

f(x) = √(x – 1) + 3

f(x) = (x + 3)2 – 2