Math-3 Semester-1 Version-2 Finals

Identify the transformations of the graph of ƒ(x) = x³ that produce the graph of the given function g(x). Then graph g(x) on the same coordinate plane as the graph of ƒ(x) by applying the transformations to the reference points (-1, -1), (0, 0), and (1, 1).

g(x) = -(x-4)³-3

8 points

Graph the function. State the end behavior, x-intercepts, y-intercept, degree n, direction of the graph (uphill, downhill, facing up or down) and intervals where the function is above or below the x-axis.

f(x) = (x+1)(x-4)(x-2)²

8 points

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Convert the equation y= x²-2x-5 into vertex form. 

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Determine the vertex of the parabola y=5(x-2)²–7

• (5, -7)

• (-2, -7)

• (2, -7)

• (-7, -2)

Identify the vertex and whether the graph opens up or down.

• (5, 2); opens up

• (5, 2); opens down

• (-5, 2); opens up

• (-5, 2); opens down

What is the vertex?

• (-1,-2)
• (-2,-1)
• (-3,-1)
• (2,1)

Which of the following is the correct equation for the given graph?

• f(x) = (x - 2)² - 1
• f(x) = (x + 2)² - 1
• f(x) = -(x + 2)² - 1
• f(x) = -(x - 2)² - 1

What are the x- intercepts?

• x= 0 and x= -4
• x= 0 and x= 4
• y= 0
• x= 2

What are the coordinates of the y-intercept?

• (0,1)

• (0,-2)

• (0,-3)

• (0,2)