Chapter 11.4, Problem 1E

(a)

To determine

To fill: Suppose we want to graph an equation on $x$ and $y$.

If we replace $x$ by $x-3$, the graph of the equation is shifted to the ____ by $3$ units. If we replace $x$ by $x+3$, the graph is shifted to the ____ by $3$ units.

Answer to Problem 1E

Suppose we want to graph an equation on $x$ and $y$.

If we replace $x$ by $x-3$ , the graph of the equation is shifted to the right by $3$ units. If we replace $x$ by $x+3$ , the graph is shifted to the left by $3$ units.

Explanation of Solution

Definition used:

Definition 1:

“If $h$ and $k$ are any two positive real numbers and a graph of any equation is in terms of $x$ and $y$ then.

(i) Replacing $x$ by $x-h$, shift the graph right to $h$ units.

(ii) Replacing $x$ by $x+h$, shift the graph left to $h$ units.

(iii) Replacing $y$ by $y-k$, shift the graph upward to $k$ units.

(iv) Replacing $y$ by $y+k$, shift the graph downward to $k$ units.”

Calculation:

By the definition $1$, It is clear that $x$ replaces by $x-h$ on a graph in terms of $x$ $\&$ $y$, shift the graph right to $h$ units, and $x$ by $x+h$, shift the graph to $h$ units left.

Hence, the graph an equation in terms of $x$ and $y$, $x$ replaces by $x-3$ shift the graph to $3$ units right and $x$ replaces by $x+3$ units, shift the graph to $3$ units left.

(b)

To determine

To fill: Suppose we want to graph an equation on $x$ and $y$.

If we replace $y$ by $y-1$, the graph of the equation is shifted to the ____ by $1$ units. If we replace $y$ by $y+1$, the graph is shifted to the ____ by $1$ units.

Answer to Problem 1E

Suppose we want to graph an equation on $x$ and $y$.

If we replace $y$ by $y-1$, the graph of the equation is shifted upward by $1$ unit. If we replace $y$ by $y+1$, the graph of the equation is shifted downward by $1$ unit.

Explanation of Solution

By the definition $1$, It is clear that $y$ replaces by $y-h$ on a graph in terms of $x$ $\&$ $y$ shift the graph upward by $h$ units, and $y$ replaces by $y+h$, shift the graph down by $h$ units.

Hence, while graph of an equation in terms of $x$ and $y$, $y$ replaces by $y-1$ shift the graph $1$ units upward and $y$ replaces by $y+1$, shift the graph $1$ unit downward.