Checkpoint: Assess Your Understanding, pages
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1 Checkpoint: Assess Your Understanding, pages Multiple Choice The graph of 3 3 is translated units right and 5 units down. What is an equation of the translation image? A. =-3( + ) B. =-3( - ) C. =-3( + ) 3-1 D. =-3( - ) 3-1 Chapter 3: Transforming Graphs of Functions Checkpoint Solutions DO NOT COPY. P
2 . Here is the graph of = g(). On the same grid, sketch the graph of each function below. State the domain and range of each function. a) - 3 = g() Compare the equation to k g(): k 3 So, mark some lattice points on g() and translate each point 3 units up. Both functions have domain: ç Both functions have range: ç g( + ) g() + 1 g( 3) 3 g() 1 b) = g( + ) Write g( ) as g( ( )). Compare the equation to g( h): h Translate each point on the graph of g() units left. The domain is: ç The range is: ç c) + 1 = g( - 3) Write 1 g( 3) as ( 1) g( 3). Compare the equation to k g( h): h 3 and k 1 Translate each point on the graph of g() 3 units right and 1 unit down. The domain is: ç The range is: ç P DO NOT COPY. Chapter 3: Transforming Graphs of Functions Checkpoint Solutions 7
3 3. The graph of = f() was translated to create each graph below. Write an equation of each graph in terms of the function f. f() a) 3 f( 5) The graph of f() has a local maimum at (, 9). This graph has a local maimum at ( 3, ). So, the graph of f() was translated 5 units left and 3 units down. The equation of the image graph has the form: k f( h), where h 5and k 3 So, an equation of the image graph is: 3 f( 5) b) 1 f( 3) 1 The graph of f() has a local maimum at (, 9). This graph has a local maimum at (5, 11). So, the graph of f() was translated 3 units right and units up. The equation of the image graph has the form: k f( h), where h 3 and k So, an equation of the image graph is: f( 3) Chapter 3: Transforming Graphs of Functions Checkpoint Solutions DO NOT COPY. P
4 3.. Multiple Choice The graph of = f() was reflected in the -ais. Which graph below is its reflection image? f() A. B. C. D. 5. Here is the graph of = k(). On the same grid, sketch and label the graph of each function below, then state its domain and range. k( ) k() a) =-k() The graph of k() is the image of the graph of k() after a reflection in the -ais. Mark some lattice points on k(), k() then reflect them in the -ais. Mark these image points, then join them. Domain: ç Range: b) = k(-) The graph of k( ) is the image of the graph of k() after a reflection in the -ais. Mark some lattice points on k(), then reflect them in the -ais. Mark these image points, then join them. Domain: ç Range:» P DO NOT COPY. Chapter 3: Transforming Graphs of Functions Checkpoint Solutions 9
5 . The graph of = was reflected in the -ais and its image is shown. What is an equation of the image? When the graph of f() is reflected in the -ais, the equation of its image is f( ). So, an equation of the image is: f( ) ( ) 3 3( ) ( ) Multiple Choice The point (, ) lies on the graph of = f(). After vertical and horizontal stretches or compressions of the graph, the equation of the image is = 3f(). Which point is the image of (, )? A. ( 3, ) B. ( 1, ) C. (, ) D. ( 1, 1). Here is the graph of = h(). On the same grid, sketch the graph of each function below, then state its domain and range. 1 h() h() a) = 1 1 h( ) 3 h(-) 3 Compare ah(b) to 1 : a 1 and b 3 h( ) 3 So, the graph of h() is verticall compressed b a factor 1 1 of, horizontall compressed b a factor of, then reflected 3 in the -ais. Use mental math and the transformation: (, ) on h() corresponds to a on 1, to, 1 3 b 3 h( ) mark some image points, then join them. Domain: ; range: 1 b) = h() Compare ah(b) to h() : a and b So, the graph of h() is verticall stretched b a factor of, and 1 horizontall compressed b a factor of. Use mental math and the transformation: (, ) on h() corresponds to a on h(),, b to mark some image points, then join them. Domain: 1 ; range: 1 3 Chapter 3: Transforming Graphs of Functions Checkpoint Solutions DO NOT COPY. P
6 9. The graph of = g() is the image of the graph of = f() after a vertical and/or horizontal stretch and/or reflection. Corresponding points are labelled. Write an equation of the image graph in terms of the function f. A B A f() 1 g() 1 B Point A(, ) on f() corresponds to point A (, ) on g(). An equation for the image graph after a vertical or horizontal stretch or compression can be written in the form af(b). A point (, ) on f() corresponds to the point a on af(b). b, ab The image of A(, ) is a which is A (, ). b, a()b, Equate the -coordinates: b 1 Equate the -coordinates: a 3 So, an equation of g() is: 3fa 1 b I used the coordinates of B and B, and mental math to verif the equation. P DO NOT COPY. Chapter 3: Transforming Graphs of Functions Checkpoint Solutions 31
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