Name: Date: Absolute Value Transformations

Transcription

1 Name: Date: Absolute Value Transformations Vocab: Absolute value is the measure of the distance awa from zero on a number line. Since absolute value is the measure of distance it can never be negative! Parent Function is the simplest form of a famil of functions Absolute value parent function is = x Transformation is a change made to a function (in the equation or graph) Vertex is the point where the graph changes directions Let s make a table and graph the absolute value parent function. x Y x What do ou notice about the graph? The point where the graph changes directions. What is the vertex of the absolute value parent function? How can ou tell from the table and graph?

2 Since we know not all equations are the same, lets explore what happens if we change the parent function. 1.) Using the graphing calculator: a.) click on apps b.) Scroll down to Transfrm (or hit alpha T ()) c.) Hit enter and then an ke to go back to the home screen Now let s tell the calculator what we want to transform! a.) go to = (notice the pause sign.this means the transform app is on) b.) tpe abs(x) + A {abs can be found in the MATH, NUM) c.) hit graph d.) Use the right and left arrows to see how the graph changes when we add or subtract a value. QUESTION: What do ou notice? QUESTION: Write a rule to explain what happens to the absolute value graph when we add or subtract a value outside the absolute value sign. QUESTION: Pick three A values and write the equation, sketch the graph, identif the vertex, and describe the transformations: x x x Equation: Equation: Equation: Transformation: Transformation: Transformation:

3 .) Now let s explore what happens when we add or subtract a value inside the absolute value sign. a.) go to = (notice the pause sign.this means the transform app is on) b.) tpe abs(x + A) c.) hit graph d.) Use the right and left arrows to see how the graph changes when we add or subtract a value. QUESTION: What do ou notice? QUESTION: Write a rule to explain what happens to the absolute value graph when we add or subtract a value inside the absolute value sign. QUESTION: Pick three A values and write the equation, sketch the graph, identif the vertex, and describe the transformations: x x x Equation: Equation: Equation: Transformation: Transformation: Transformation:

4 3.) Now let s explore what happens when multipl the absolute value b a coefficient. a.) go to = (notice the pause sign.this means the transform app is on) b.) tpe A abs(x) c.) hit graph e.) Use the right and left arrows to see how the graph changes when we multipl b a coefficient QUESTION: What do ou notice? QUESTION: Write a rule to explain what happens to the absolute value graph when we multipl the absolute value parent function b a coefficient QUESTION: What happens to the graph when A becomes negative? Write a rule to describe the effects of a negative a value. REFLECTION OVER X-AXIS: QUESTION: Pick three A values and write the equation, sketch the graph, identif the vertex, and describe the transformations: x x x Equation: Equation: Equation: Transformation: Transformation: Transformation:

5 Putting it all together: The general form of an absolute value function is: Identif the effects of each parameter: A: = a x + h + k H: K: Example: Describe the transformations of each absolute value equation: a.) = x b.) = ½ x c.) = x d.) = - x Example: Write the equation of each absolute function that has the following transformations: a.) Vertex is (,1) b.) vertex is (-,3) and has a vertical dilation and a stretch b 3 c.) vertex (-3, 0) and reflected over x axis d.) vertex is (-1, -) with a reflection over x axis e.) vertex at origin, vertical dilation b /3

6 Now let s graph an absolute value function without using the graphing calculator. 1.) Start b writing down all the transformations.) Move our translations (plot our vertex) 3.) Appl and vertical dilations and reflections.) Connect the points to make a smooth curve Example: Graph the absolute value equation = - x + 3 Graph: We can answer all our function questions using our graph! a.) Is this a function? Explain: b.) What is the domain: x c.) What is the range: d.) What is the x intercept: e.) What is the intercept: f.) Is there a max or min? If so, what is it? g.) Where is it? h.) Describe the end behavior: a. As x, b. As x, i.) What are the zero(s)? j.) Interval increasing: k.) Interval decreasing:

7 You tr: Graph each absolute value function and answer all the function questions! a.) f(x) = ½ x 3-1 b.) = -3 x + c.) f(x) = -/3 x + x x x Question Graph a Graph b Graph c Is it a function? Explain. Domain: Range: X intercept: Y intercept: Zeros: Interval increasing: Interval decreasing: Max/Min: End Behavior: As x, As x -, Transformations

8 Now let s reverse the process! For each graph, describe all transformations and write the equation! a.) a.) b.) Equation: Equation: c.) d.) Equation: Equation: