MAT 136 Exam 2 With 100% Verified Solutions 2025

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. f(g(x)) = evaluate f (x2 + 9) by substituting the value of g into f f (x2 + 9) = √x2 + 9 + 8 g(f(x)) = Evaluate g(√x + 8 ) by subsitiuting in the value of f into g g (√x + 8 ) = (√x + 8)2 + 9 g (√x + 8 ) = (√x + 8)(√x + 8) + 9 expand (√x + 8 )(√x + 8 ) using the FOIL method g(√x + 8 = x + 16√x + 64 + 9 g(f(x)) = x + 16√x + 73 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). 2/27/2023 Southern New Hampshire University - Gradebook 3/30 0/0.0 Question g(f(x)) = (√x + 8 )2 + 9 = x + 16√x + 64 + 9 = x + 16√x + 73 Q2 View Original Response Unfiltered Response Auto graded Grade: 1/1.0 of Your response Correct response 10 10 Auto graded Grade: 1/1.0 units A horizontal shift Your response Correct response right right Auto graded Grade: 1/1.0 of Your response Correct response 6 6 1 The graph of the function f(x) = x - 6 + 10 is a transformation of the graph of the function 1 g(x) = x by A vertical shift Your response Correct response up up 2/27/2023 Southern New Hampshire University - Gradebook 4/30 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 Analyze the graph of the function f(x) = 2|x + 5| + 8 compared to the graph of the absolute value function g(x) = |x| . To obtain the graph of f(x) = 2|x + 5| + 8, the graph of g(x) = |x| has been Shifted Your response Correct response left left 2/27/2023 Southern New Hampshire University - Gradebook 5/30 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 2/27/2023 Southern New Hampshire University - Gradebook 6/30 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. 2/27/2023 Southern New Hampshire University - Gradebook 7/30 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. Solve the equation. |4x + 7| − 3 = 21 Enter the exact answers. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or x + 1; x − 1). The order of the list does not matter. x = Your response Correct response 17/4; -31/4 -31/4;17/4 2/27/2023 Southern New Hampshire University - Gradebook 8/30 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 Ungraded Grade: 0/1.0 Total grade: 1.0×1/2 + 0.0×1/2 = 50% + 0% Feedback: Isolate the absolute value expression and then write two equations. |4x + 7| − 3 = 21 |4x + 7| = 24 4x + 7 = − 24 4x + 7 = 24 4x = − 31 4x = 17 31 17 x = − 4 x = 4 31 17 There are two solutions: − 4 and 4 . 2/27/2023 Southern New Hampshire University - Gradebook 9/30 Question Q5 0/0.0 View Original Response Unfiltered Response Write an equation for the line graphed below From the graph, you can see that (-2, 0) and (0, 4) are two points on this line. y = Your response Correct response 2 x + 4 2*x+4 Auto graded Grade: 1/1.0 2/27/2023 Southern New Hampshire University - Gradebook 10/30 Slope intercept form is y=mx+b b is the y intercept when x=0, on our graph this is (0,4), so b = 4 m is the slope which is rise over run. Our graph's rise is 2 and the run is 1 so 2/1 =2, m=2 y = 2 x + 4 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: 1.0×1/2 + 0.0×1/2 = 50% + 0% Feedback: We can use the slope formula to find the slope of the line using the points (-2, 0) and (0, 4). rise m = run 4 = 2 = 2 We can substitute the slope and the coordinates of one of the points into slope-intercept form. 2/27/2023 Southern New Hampshire University - Gradebook 11/30 Question 4 = 2(0) + b 4 = 0 + b b = 4 Therefore the equation of the line is y = 2x + 4. Q6 0/0.0 View Original Response Unfiltered Response Auto graded Grade: 1/1.0 in 2016. 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. If we take 76,000 - 57,000 = 19,000 and divide that by 2 we get 9,500 people per x years. Our equation becomes 9500x+57000 (9500*6)+57000=114000 there are six years from 2010 to 2016 so x=6 Ungraded Grade: 0/1.0 A town’s population increases at a constant rate. In 2010 the population was 57,000. By 2012 the population had increased to 76,000. If this trend continues, predict the population in 2016. The population will be Your response Correct response 114000 114,000 2/27/2023 Southern New Hampshire University - Gradebook 12/30 Question Total grade: 1.0×1/2 + 0.0×1/2 = 50% + 0% Feedback: We define our input as the number of years since 2010: Input: t, years since 2010 Output: P(t), the town's population To predict the population in 2016 (t = 6), we would first need an equation for the population. To write an equation, we need the initial value and the rate of change, or slope. To determine the rate of change, we will use the change in output per change in input. The problem gives us two input-output pairs (0, 57000) and (2, 76000) that we can use to calculate the slope. change in output m = change in input 76,000 − 57,000 = 2 − 0 19,000 = 2 = 9,500 people per year We already know the y-intercept of the line, so we can immediately write the equation: P(t) = 9,500t + 57,000 2/27/2023 Southern New Hampshire University - Gradebook 13/30 Question To predict the population in 2016, we evaluate our function at t = 6. P(6) = 9,500(6) + 57,000 = 57,000 + 57,000 = 114,000 If the trend continues, our model predicts a population of 114,000 in 2016.