Graphing absolute value functions and transformations Math 2: Unit 5B Day 2 Graphing absolute value functions and transformations

Absolute Value Parent Function

Transformations and translations of the parent function The graph has vertex (h,k) and is symmetric in the line x = h h shifts the parent function horizontally (remember to change the sign) k shifts the parent function vertically The graph is V-shaped. It opens up if a > 0 and down if a < 0. The graph is wider than the graph of if < 1 and narrower if >1.

Transformations and translations of the parent function

Identify the vertex, tell whether the graph opens up or down, then tell whether the graph is wider or narrow or normal compared to Vertex (-3,-5), opens up, Narrower. Vertex (0,-5), opens up, Wider.

Identify the vertex, tell whether the graph opens up or down, then tell whether the graph is wider or narrow or normal compared to Vertex (5,-2), opens down, Narrower. Vertex (½,4), opens up, Normal or the same. Vertex (5,0), opens down, Normal or the same.

Intercepts To find the x-intercept(s): substitute in 0 for y To find the y-intercept: substitute in 0 for x From a graph, the intercepts are where the graph crosses each axis. No x-intercepts! y-intercept (0,-2)

Domain and Range Domain (x-values): read from left to right Range (y-values): read from bottom to top Find the domain and range of this function. Domain: all real numbers Range: y ≥ 2.

Domain and Range Domain (x-values): read from left to right Range (y-values): read from bottom to top Find the domain and range of this function. Domain: all real numbers Range: y ≥ - 4 .

Domain and Range Domain (x-values): read from left to right Range (y-values): read from bottom to top Find the domain and range of this function. Domain: all real numbers Range: y ≤ - 1 .

Zeros The values of x when f(x) = 0 To find the zeros of any function: plug in y = 0 and solve for x. Find the zero(s) of x = -1 and x = 3 .

Intervals of increasing and decreasing Find the intervals where this function is increasing and decreasing. Decreases: Increases: Decreases: (-∞, -3) Increases: (-3,∞)

Intervals of increasing and decreasing Find the intervals where this function is increasing and decreasing. Decreases: Increases: Decreases: (-∞, 2) Increases: (2,∞)

Intervals of increasing and decreasing Find the intervals where this function is increasing and decreasing. Decreases: Increases: Increases: (-∞, -2) Decreases: (-2,∞)

Graphing To graph an absolute value function Find the vertex and sketch the AOS Use a table of values choosing 2 x-values on each side of the vertex plot the points and draw the graph

Graphing Vertex: Max/min? Axis of symmetry: Domain: Range: Y-intercept: Zeros: Intervals of increase and decrease ( - 2, - 1) minimum x = - 2 all real numbers y ≥ - 1 . ( 0, 1) ( -3, 0) and ( -1, 0) Decreases: (-∞, -2) Increases: (-2,∞)

Graph the following: Vertex: Max/min? AOS: Domain: Range: Intercepts: Zeros: Intervals of increase and decrease x y

Graph the following: Vertex: AOS: Domain: Range: Intercepts: Zeros: Intervals of increase and decrease x y

Graph the following: Vertex: Max/min? AOS: Domain: Range: Intercepts: Zeros: Intervals of increase and decrease x y

Slope is the average rate of change! Calculating average rate of change Do you remember how to find slope when given 2 points? If you know any two points on a line, or two solutions of a linear equation, you can find the slope of the line without graphing. Slope is the average rate of change! 20

On the following graph, where is the rate of change positive On the following graph, where is the rate of change positive? Where is it negative? Tell about the interval:

On the following graph, where is the rate of change positive On the following graph, where is the rate of change positive? Where is it negative? Tell about the interval:

Assignment: Handout