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**Graphing absolute value functions and transformations**

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

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**Absolute Value Parent Function**

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**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.

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**Transformations and translations of the parent function**

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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.

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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.

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**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)

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**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.

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**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 .

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**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 .

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**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 .

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**Intervals of increasing and decreasing**

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

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**Intervals of increasing and decreasing**

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

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**Intervals of increasing and decreasing**

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

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**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

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**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,∞)

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**Graph the following: Vertex: Max/min? AOS: Domain: Range: Intercepts:**

Zeros: Intervals of increase and decrease x y

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**Graph the following: Vertex: AOS: Domain: Range: Intercepts: Zeros:**

Intervals of increase and decrease x y

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**Graph the following: Vertex: Max/min? AOS: Domain: Range: Intercepts:**

Zeros: Intervals of increase and decrease x y

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**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

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**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:

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**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:

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Assignment: Handout

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