MAT 136

Question Show your work and explain how you arrived at your answer. Answers with no relevant explanations do not show an understanding of the topic and may get reduced or no credit. Ungraded Grade: 0/1.0 Total grade: 1.0×1/3 + 1.0×1/3 + 0.0×1/3 = 33% + 33% + 0% Feedback: Let's begin by substituting g(x) into f(x). f(g(x)) = √(x2 + 9) + 8 = √x2 + 9 + 8 Now we can substitute f(x) into g(x). Question g(f(x)) = (√x + 8 )2 + 9 = x + 16√x + 64 + 9 = x + 16√x + 73 Q2 0/0.0 View Original Response Unfiltered Response Auto graded Grade: 1/1.0 of Your response Correct response 10 10 Auto graded Grade: 1/1.0 Auto graded Grade: 1/1.0 of Your response Correct response 6 6 Question Auto graded Grade: 1/1.0 units Show your work and explain how you arrived at your answer. Answers with no relevant explanations do not show an understanding of the topic and may get reduced or no credit. When you graph both functions you can see the transformation graph is shifted 10 units up on the y axis and six units to the right on the x axis from the original To graph y = f(x − h), shift the graph of y = f(x) right h units by adding h to the x coordinates of the points on the graph of f To graph y = f(x) + k, shift the graph of y = f(x) up k units by adding k to the y coordinates of the points on the graph of f Ungraded Grade: 0/1.0 Total grade: 1.0×1/5 + 1.0×1/5 + 1.0×1/5 + 1.0×1/5 + 0.0×1/5 = 20% + 20% + 20% + 20% + 0% Feedback: 1 The graph of the function g(x) = x is centered at the origin. The graph of the translated function 1 f(x) = x - 6 + 10 is the graph of g(x) shifted up 10 units and right 6 units. The graph of f(x) is centered at (+ 6, + 10) as x can not be equal to + 6 and y can not be equal to + 10. Q3 0/0.0 View Original Response Unfiltered Response Auto graded Grade: 1/1.0 Question by Your response Correct response 5 5 Auto graded Grade: 1/1.0 units Shifted Your response Correct response up up Auto graded Grade: 1/1.0 by Your response Correct response 8 8 Auto graded Grade: 1/1.0 units Vertically stretched by a factor of Your response Correct response 2 2 Auto graded Grade: 1/1.0 Which of the following best represents the graph of this function, considering the location (quadrant) of the vertex and the direction that the graph opens? Your response Correct response Question Auto graded Grade: 1/1.0 Show your work and explain how you arrived at your answer. Answers with no relevant explanations do not show an understanding of the topic and may get reduced or no credit. To graph y = f(x + h), shift the graph of y = f(x) left h units by subtracting h from the x coordinates of the points on the graph of f To graph y = f(x) + k, shift the graph of y = f(x) up k units by adding k to the y coordinates of the points on the graph of f to graph y = af(x), multiply all the y coordinates of the points on the graph of f by a. The graph of f has been vertically scaled by a factor of a. If a 1, the graph of f has undergone a vertical stratching by a factor of a Ungraded Grade: 0/1.0 Total grade: 1.0×1/7 + 1.0×1/7 + 1.0×1/7 + 1.0×1/7 + 1.0×1/7 + 1.0×1/7 + 0.0×1/7 = 14% + 14% + 14% + 14% + 14% + 14% + 0% Feedback: The corner point, or vertex, of f(x) = 2|x + 5| + 8 is where the expression x + 5 is 0, i.e. when x = − 5. This means that the graph of g(x) = |x| has been shifted left by 5 units. At the corner point where x = − 5, the function f(x) is equal to 8. This means that the graph of g(x) = |x| has been shifted up by 8 units. Question The coefficient 2 in f(x) = 2|x + 5| + 8 means that the graph of g(x) = |x| has been stretched by a factor of 2 . We know that the toolkit function g(x) = |x| opens upwards from the origin. Since the stretching factor of 2 is positive, the graph of f(x) = 2|x + 5| + 8 also opens upwards. Since f(x) = 2|x + 5| + 8 is g(x) shifted left by 5 units and upwards by 8 units, the corner or vertex is in the second quadrant. Q4 0/0.0 View Original Response Unfiltered Response Auto graded Grade: 1/1.0 Show your work and explain how you arrived at your answer. Answers with no relevant explanations do not show an understanding of the topic and may get reduced or no credit. Question |4 x + 7| = 21 + 3 move all terms not containing |4 x + 7| to the right side of the equation |4 x + 7| = 24 4 x + 7 = ± 24 remove the absolute value term which creates a ± on the right side of the equation because |x| = ± x 4 x + 7 = 24 First solve for positive portion of solution 4 x = 24 − 7 4 x = 17 17 x = 4 4 x + 7 = − 24 Next solve for negative portion 4 x = − 24 − 7 4 x = − 31 31 x = − 4