In part A and B, fill in the blanks. (Hint: Each long tick mark represents one u

Question

In part A and B, fill in the blanks.

(Hint: Each long tick mark represents one unit. Therefore, the first piece of the graph of f is a line containing the points (-3,2) and (-1,2), while the second piece is a line containing the points (-1,2) and (1,0). How do you find the equation of the line?)

c. Determine the range of f in interval notation.

d. Which of the following is correct?

Graph 1: f(a) Graph 2: g(x) You're given the information that Graphs 1 and 2 are piecewise linear, and that Graph 2 is a transformation of Graph 1 using horizontal and vertical translations.

Explanation / Answer

The first graph:

The line , where -3 x -1,  in the first graph, passes through the points ( -3,2) and (-1,2) is horizontal. Its slope is 0. Therefore, its equation is of the type y = c, wherec is a constant. Since it passes throgh  the point ( -3,2) and (-1,2), its equation is y = f(x) = 2.

The line , where -1 x 1,  in the first graph, passes through the points ( -1, 2) and (1,0). Its slope is (2- 0)/( -1-1) = 2/-2 = -1. Also, this line's y -intercept is 1 ( y-intercept is where x = 0).Therefore, its equation is y = f (x) = -x + 1. intercept.

c. The range of, for the line where -3 x -1 is [ 2 ] as y is constant. The range of, for the line where -1 x 1 is [ 0, 2]

d. The 2nd graph is a shift of the 1st graph to the right by 3 units and upwards by 1 unit.Therefore, g(x) = f(x + 3)+ 1. The option C is correct.

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