MAT 136 Exam 2 With 100% Verified Solutions 2025

- View Panel Style - Student Details 7-3 Exam Two Score: Page: 1 of 1 Rows: 1 - 12 of 12 - 0 Q1 Question View Original Response Unfiltered Response Use the pair of functions to find f (g (x)) and g (f (x)). Simplify your answers. f (x) = √x + 6, g (x) = x2 + 9 f (g (x)) = Your response Correct response sqrt(x^2+9) + 6 sqrt(x^2+9)+6 Auto graded Grade: 1/1.0 g (f (x)) = Your response Correct response x+12sqrt(x)+45 x+12*sqrt(x)+45 Auto graded Grade: 1/1.0 Show your work and explain how you arrived at your answer. Answers with no releva 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: Numeric 0/0.0 Southern New Hampshire University - Gradebook 2/20 Question Let's begin by substituting g (x) into f (x). f (g (x)) = √(x2 + 9) + 6 = √x2 + 9 + 6 Now we can substitute f (x) into g (x). g (f (x)) = (√x + 6)2 + 9 = x + 12√x + 36 + 9 = x + 12√x + 45 Southern New Hampshire University - Gradebook 3/20 0/0.0 0/0.0 Question 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 4 4 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: The graph of the function g (x) = 1 is centered at the origin. The graph of the translated functi 1 x f (x) = x − 4 — 10 is the graph of g (x) shifted down 10 units and right 4 units. The graph f (x) is centered at (+ 4, − 10) as x can not be equal to + 4 and y can not be equal to − 10. Q3 View Original Response Unfiltered Response Auto graded Grade: 1/1.0 units Show your work and explain how you arrived at your answer. Answers with no releva explanations do not show an understanding of the topic and may get reduced or no credit. The graph of the function g(x)=1/x is centered at the origin. The graph of the function is f(x)=1/(x-4) -10. The g(x) is shifted "down" 10 unit (because it is negative) and right 4 units (negative moves to the right). The graph of f(x) is centered at ( 4,-10). The "x" intercept can't be equal to 4 and "y" intercept can't be equal to -10. The graph of the function f (x) = 1 − 10 is a transformation of the graph of the functio 1 x − 4 g (x) = by x A vertical shift Your response Correct response down down Analyze the graph of the function f (x) = 4 |x + 7| + 10 compared to the graph of the absolu value function g (x) = |x| . To obtain the graph of f (x) = 4 |x + 7| + 10, the graph of g (x) = |x| has been Shifted Your response Correct response Southern New Hampshire University - Gradebook 4/20 Question left left Auto graded Grade: 1/1.0 by Your response Correct response 7 7 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 10 10 Auto graded Grade: 1/1.0 units Vertically stretched by a factor of Your response Correct response 4 4 Auto graded Grade: 1/1.0 Which of the following best represents the graph of this function, considering the locatio (quadrant) of the vertex and the direction that the graph opens? Your response Correct response Auto graded Grade: 1/1.0 Show your work and explain how you arrived at your answer. Answers with no releva explanations do not show an understanding of the topic and may get reduced or no credit. The corner point or vertex of f(x) =4 abs(x+7) + 10, where abs(x+7) has been shifted "left" by 7 units. The function f(x) is equal to 10, which means the graph of g(x) = abs(x) shifts "up" 10 units. The coefficient 4 in f(x)=4abs(x+7) + 10 means that the graph g(x) = abs(x) is "stretched" by a factor 4. The function g(x) = abs(x) opens upwards because it has a stretch factor of 4 which is positive. The graph of f(x) =4 abs(x+7) + 10 opens "upwards." Now we know that f(x) =4 abs(x+7) + 10, the g(x) shifted "left" by 7 units, "upwards" by 10 units, the corner or vertex is located in the "second" quadrant. Ungraded Grade: 0/1.0 Southern New Hampshire University - Gradebook Question 5/20 0/0.0 Show your work and explain how you arrived at your answer. Answers with no releva explanations do not show an understanding of the topic and may get reduced or no credit. 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) = 4 |x + 7| + 10 is where the expression x + 7 when x = −7. This means that the graph of g (x) = |x| has been shifted left by 7 units. is 0, At the corner point where x = −7, the function f (x) is equal to 10. This means that the graph g (x) = |x| has been shifted up by 10 units. The coefficient 4 in f (x) = 4 |x + 7| + 10 means that the graph of g (x) = |x| has been stretc by a factor of 4 . We know that the toolkit function g (x) = |x| opens upwards from the origin. Since the stretch factor of 4 is positive, the graph of f (x) = 4 |x + 7| + 10 also opens upwards. Since f (x) = 4 |x + 7| + 10 is g (x) shifted left by 7 units and upwards by 10 units, the corner vertex is in the second quadrant. Q4 View Original Response Unfiltered Response Auto graded Grade: 1/1.0 Solve the equation. |2x + 5| − 6 = 4 Enter the exact answers. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 x + 1; x − 1). The order of the list does not matter. x = Your response Correct response 5/2;-15/2 -15/2;5/2 Southern New Hampshire University - Gradebook Question 6/20 0/0.0 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. |2x + 5| − 6 = 4 |2x + 5| = 10 2x + 5 = −10 2x + 5 = 10 2x = −15 2x = 5 x = − 15 2 x = 5 2 There are two solutions: − 15 and 5 . 2 2 Q5 View Original Response Unfiltered Response Solve abs(2x+5)-6=4 abs(2x+5)=4+6 -> Simplify by adding 6 on both sides 2x+5=±10 -> remove absolute value term which creates ± on the right side of the equation because abs(x)=±x 2x+5=+10 -> Solve for positive part of the solution 2x=10 - 5 -> Simplify by adding 5 on both sides 2x=5 -> Simplify subraction 2x/2=5/2 -> Simplify by diving 2 on both sides x=5/2 -> ANSWER 2x+5=-10 -> Solve for negative part of the solution 2x= -10 - 5 -> Simplify by adding 5 on both sides 2x= -15 -> Simplify addition 2x/2= -15/2 -> Simplify by diving 2 on both sides x= -15/2 -> ANSWER Southern New Hampshire University - Gradebook 7/20 Feedback: Given the slope of the line (0,-1) and (1,3), we can use the m=rise/run formula: m=rise/run m=y2-y1/x2-x1 m=3-(-1)/1-0 -> Substitute (0,-1) and (1,3) to m=y2-y1/x2-x1 m=3+1/1 -> Simplify parentheses m=4/1 -> Simplify addition m=4 -> Simplify division m=4 -> ANSWER for value of the slope or "m" in formula y=mx+b Now we can substitute the slope and the coordinates of one of the points to the slope-intercept formula of y=mx+b. y=mx+b 3=4(0)+b -> Substitute y=4, m=4, x=0 3=0+b -> Simplify parentheses b=3 -> ANSWER for the value of b in formula y=mx+b Therefore the equation (formula y=mx+b) of the line y = 4x+3 Question Write an equation for the line graphed below From the graph, you can see that (0, −1) and (1, −3) are two points on this line. y = Your response Correct response 4*x+3 -2*x-1 Auto graded Grade: 0/1.0 Show your work and explain how you arrived at your answer. Answers with no releva explanations do not show an understanding of the topic and may get reduced or no credit. Ungraded Grade: 0/1.0 Total grade: 0.0×1/2 + 0.0×1/2 = 0% + 0%