Chapter 1, Problem 11RCC

(a)

To determine

To write: The equation of the graph which is obtained from the given graph such that the graph is shifted 2 units upward.

Answer to Problem 11RCC

Solution:

The equation of the graph of f becomes $y=f\left(x\right)+2$.

Explanation of Solution

Let the equation of the graph be $y=f\left(x\right)$.

Since the graph is vertically (upward) shifted, add 2 to the $f\left(x\right)$.

Thus, the equation of the graph of f becomes $y=f\left(x\right)+2$.

(b)

To determine

To write: The equation of the graph which is obtained from the given graph such that the graph is shifted 2 units downward.

Answer to Problem 11RCC

Solution:

The equation of the graph of f becomes $y=f\left(x\right)-2$.

Explanation of Solution

Let the equation of the graph be $y=f\left(x\right)$.

Since the graph is vertically (upward) shifted, subtract 2 from the $f\left(x\right)$.

Thus, the equation of the graph of f becomes $y=f\left(x\right)-2$.

(c)

To determine

To write: The equation of the graph which is obtained from the given graph such that the graph is shifted 2 units to the right side.

Answer to Problem 11RCC

Solution:

The equation of the graph of f becomes $y=f\left(x-2\right)$.

Explanation of Solution

Let the equation of the graph be $y=f\left(x\right)$.

Since the graph is horizontally (right side) shifted, subtract 2 from x.

Thus, the equation of the graph of f becomes $y=f\left(x-2\right)$.

(d)

To determine

To write: The equation of the graph which is obtained from the given graph such that the graph is shifted 2 units to the left side.

Answer to Problem 11RCC

Solution:

The equation of the graph of f becomes $y=f\left(x+2\right)$.

Explanation of Solution

Let the equation of the graph be $y=f\left(x\right)$.

Since the graph is horizontally (left side) shifted, add 2 to x.

Thus, the equation of the graph of f becomes $y=f\left(x+2\right)$.

(e)

To determine

To write: The equation of the graph which is obtained from the given graph such that the graph reflects about the x axis.

Answer to Problem 11RCC

Solution:

The equation of the graph of f becomes $y=-f\left(x\right)$.

Explanation of Solution

Let the equation of the graph be $y=f\left(x\right)$.

Since the graph is reflecting about the x-axis, the obtained graph must be an odd function.

Therefore, substitute $f\left(x\right)$ by $-f\left(x\right)$.

Thus, the equation of the graph of f becomes $y=-f\left(x\right)$.

(f)

To determine

To write: The equation of the graph which is obtained from the given graph such that the graph reflects about the y axis.

Answer to Problem 11RCC

Solution:

The equation of the graph of f becomes $y=f\left(-x\right)$.

Explanation of Solution

Let the equation of the graph be $y=f\left(x\right)$.

Since the graph reflects about the x-axis, the obtained graph must be an even function.

Therefore, substitute $f\left(x\right)$ by $f\left(-x\right)$.

Thus, the equation of the graph of f becomes $y=f\left(-x\right)$.

(g)

To determine

To write: The equation of the graph which is obtained from the given graph such that the graph stretched vertically by a factor of 2.

Answer to Problem 11RCC

Solution:

The equation of the graph of f becomes $y=2f\left(x\right)$.

Explanation of Solution

Let the equation of the graph be $y=f\left(x\right)$.

Since the graph is stretched vertically by a factor of 2, multiply 2 to the $f\left(x\right)$.

Thus, the equation of the graph of f becomes $y=2f\left(x\right)$.

(h)

To determine

To write: The equation of the graph which is obtained from the given graph such that the graph shrunk vertically by a factor of 2.

Answer to Problem 11RCC

Solution:

The equation of the graph of f becomes $y=\frac{f\left(x\right)}{2}$.

Explanation of Solution

Let the equation of the graph be $y=f\left(x\right)$.

Since the graph is shrunk vertically by a factor of 2, divide 2 to the $f\left(x\right)$.

Thus, the equation of the graph of f becomes $y=\frac{f\left(x\right)}{2}$.

(i)

To determine

To write: The equation of the graph which is obtained from the given graph such that the graph stretched horizontally by a factor of 2.

Answer to Problem 11RCC

Solution:

The equation of the graph of f becomes $y=f\left(\frac{x}{2}\right)$.

Explanation of Solution

Let the equation of the graph be $y=f\left(x\right)$.

Since the graph is stretched horizontally by a factor of 2, divide x by 2.

Thus, the equation of the graph of f becomes $y=f\left(\frac{x}{2}\right)$.

(j)

To determine

To write: The equation of the graph which is obtained from the given graph such that the graph shrunk horizontally by a factor of 2.

Answer to Problem 11RCC

Solution:

The equation of the graph of f becomes $y=f\left(2x\right)$.

Explanation of Solution

Let the equation of the graph be $y=f\left(x\right)$.

Since the graph is shrunk horizontally by a factor of 2, multiply $x$ by 2.

Thus, the equation of the graph of f becomes $y=f\left(2x\right)$.