Question

The graph of a function f is illustrated. Use the graph of  f as the first step toward graphing of the following function.

(a) F (x) = f (x) + 3     (b) G (x) = f (x + 2)      (c) P (x) = - f (x)     (d) H (x) = f (x + 1) - 2      (e) Q (x) = 1/2 f (x)

(f) g (x) = f (- x)          (g) h (x) = f (2 x)

Answer 1

Step 1:

Points on the graph of the function are , , and .

(a)

The function is .

To obtain the graph of , shift the graph by 3 units upward.

Determine the points by substituting .

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Graph :

Graph the function .

(1) Draw the coordinate plane.

(2) Plot the points.

(3) Connect the plotted points.

Step 2:

(b)

The function is .

To obtain the graph of , shift the graph by 2 units to the left.

Determine the points by substituting .

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.

.

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Graph :

Graph the function .

(1) Draw the coordinate plane.

(2) Plot the points.

(3) Connect the plotted points.

 

Solution :

Graph of the function .

Graph of the function .

 

Answer 2

Step 1:

Points on the graph of the function are , , and .

(c)

The function is .

To obtain the graph of , reflects the graph about the axis.

Determine the points by substituting .

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.

.

.

Graph :

Graph the function .

(1) Draw the coordinate plane.

(2) Plot the points.

(3) Connect the plotted points.

Step 2:

(d)

The function is .

To obtain the graph of , shifts the graph by 2 units downward and 1 unit towards left.

Determine the points by substituting and .

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.

.

.

Graph :

Graph the function .

(1) Draw the coordinate plane.

(2) Plot the points.

(3) Connect the plotted points.

Solution :

Graph of the function .

Graph of the function .

Answer 3

Step 1:

Points on the graph of the function are , , and .

(e)

The function is .

To obtain the graph , shrink the graph vertically by a factor of 2.

Determine the points by substituting .

.

.

.

.

Graph :

Graph the function .

(1) Draw the coordinate plane.

(2) Plot the points.

(3) Connect the plotted points.

Step 2:

(f)

The function is .

To obtain the graph , reflect the graph of about the axis.

Determine the points by substituting .

.

.

.

.

Graph :

Graph the function .

(1) Draw the coordinate plane.

(2) Plot the points.

(3) Connect the plotted points.

Solution :

(e) Graph of the function .

(f) Graph of the function .

Answer 4

Step 1:

Points on the graph of the function are , , and .

(g)

The function is .

To obtain the graph , shrink the graph horizontally by a factor of 2.

Determine the points by substituting .

.

.

.

.

Graph :

Graph the function .

(1) Draw the coordinate plane.

(2) Plot the points.

(3) Connect the plotted points.

Solution :

(g) Graph of the function .