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EXAMPLE 1

EXAMPLE 1. Graph a function of the form y = | x – h | + k. Graph y = | x + 4 | – 2 . Compare the graph with the graph of y = | x |. SOLUTION. STEP 1. Identify and plot the vertex, ( h, k ) = (–4, –2). STEP 2. Plot another point on the graph, such as (–2 , 0) . Use symmetry to

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EXAMPLE 1

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  1. EXAMPLE 1 Graph a function of the form y=| x–h |+k Graph y=|x+4|–2. Compare the graph with the graph of y=|x |. SOLUTION STEP1 Identify and plot the vertex, (h, k)=(–4, –2). STEP2 Plot another point on the graph, such as (–2, 0). Use symmetry to plot a third point, (–6, 0).

  2. EXAMPLE 1 Graph a function of the form y=| x–h |+k STEP3 Connect the points with a V-shaped graph. STEP4 Compare with y=|x|. The graph of y=|x+4 |–2 is the graph of y=|x| translated down 2 units and left 4 units.

  3. Graph (a)y=|x| and (b) y =–3|x|. Compare each graph with the graph of y=|x|. • The graph of y=|x| is the graph of y=|x| • vertically shrunk by a factor of . The graph has • vertex (0, 0) and passes through (–4, 2) and (4, 2). 1 1 1 2 2 2 EXAMPLE 2 Graph functions of the form y=a |x| SOLUTION

  4. EXAMPLE 2 Graph functions of the form y = a |x| • The graph of y=–3|x| is the graph of y=|x| vertically stretched by a factor of 3 and then reflected in the x-axis. The graph has vertex (0, 0) and passes through (–1, –3) and (1, –3).

  5. Graph a function of the form y = a x – h + k Graph y = –2 x – 1 + 3. Compare the graph with the graph of y = x . EXAMPLE 3 SOLUTION STEP1 Identify and plot the vertex, (h, k) = (1, 3). STEP2 Plot another point on the graph, such as (0, 1). Use symmetry to plot a third point, (2, 1).

  6. Graph a function of the form y = a x – h + k Compare with y = x . The graph of y = – 2 x – 1 + 3 is the graph of y = xstretched vertically by a factor of 2, then reflected in the x-axis, and finally translated right 1unit and up 3 units. EXAMPLE 3 STEP3 Connect the points with a V-shaped graph. STEP4

  7. for Examples 1, 2 and 3 GUIDED PRACTICE Graph the function. Compare the graph with the graph of y = |x|. 1.y = |x – 2| + 5 ANSWER The graph is translated right 2 units and up 5 units

  8. 2. y = |x| The graph is shrunk vertically by a factor of 1 1 4 4 for Examples 1, 2 and 3 GUIDED PRACTICE Graph the function. Compare the graph with the graph of y = |x|. ANSWER

  9. for Examples 1, 2 and 3 GUIDED PRACTICE Graph the function. Compare the graph with the graph of y = |x|. 3. f (x) = – 3| x + 1| – 2 ANSWER The graph is reflected over the x-axis,stretched by a factor of 3, translated left 1 unit and down 2 units

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