The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x): A graph with two linear functions; f of x passes through 0, negative 1 and 5, 14, and g of x passes through negative 6, negative 1 and negative 1, 14. Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points) Part B: Solve for k in each type of transformation. (4 points) Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)

9514 1404 393

  A)  vertical shift or horizontal shift

  B)  vertical shift by 18; horizontal shift by -6

  C)  horizontal: g(x) = f(x -h) . . . . shift right h units

     vertical: g(x) = f(x) +k . . . . shift up k units

Step-by-step explanation:

The graph shows that f(x) has a slope of 3 and a y-intercept of -1, so its equation is ...

  f(x) = 3x -1

Similarly, the graph of g(x) has a slope of 3 and a y-intercept of +17, so its equation is ...

  g(x) = 3x +17

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A. One linear function can be mapped to a parallel linear function by ...

Here, the two types of interest are horizontal shift, and vertical shift.

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B. We can write the vertical shift as ...

  g(x) = f(x) +k

  3x +17 = 3x -1 +k

  18 = k . . . . . . . . . add 1-3x to both sides

The "k" value for the vertical shift is 18.

We can write the horizontal shift as ...

  g(x) = f(x -k)

  3x +17 = 3(x -k) -1

  3x +17 = 3x -3k -1 . . . eliminate parentheses

  18 = -3k . . . . . . . . . . . add -13x to both sides

  -6 = k . . . . . . . . . . . . . divide by -3

The "k" value for the horizontal shift is -6.

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C. The equations are show above. Here they are again.

Horizontal shift to the right by h:

  g(x) = f(x -h)

Vertical shift up by k:

  g(x) = f(x) +k