Question

Discuss: Four Ways to Represent a Function In the box on page 154 we represented four different functions verbally, algebraically, visually, and numerically. Think of a function that can be represented in all four ways, and give the four representations.

Short answer

Verbally: Function definition is “from x subtract 4 and square it and add three”

Algebraically: The function is defined as $f\left(x\right)={\left(x-4\right)}^2+3$.

Visually:

Numerically:

$x$	$f\left(x\right)$
0 2 4 6	19 7 3 7

Step-by-step solution

Step 1. Use the definition of functions.

A function is defined as, given a set of inputs X and a set of possible outputs Y as a set of ordered pairs (x, y). We can write the statement that f is a function from X to Y using the function notationf: $X\to Y$.

Step 2. Analyze the information given.

It is given that a Function can be represented four different functions verbally, algebraically, visually, and numerically.

Step 3. Construct an example of a function.

Suppose our hypothetical function is defined as $f\left(x\right)={\left(-4\right)}^2+3$, here 4 is subtracted from the variable x and then result is squared and lastly 3 is being added.

Step 4. define the function verbally.

We can say that function definition is “from x subtract 4 and square it and add three”

Step 5. define the function algebraically.

The function is defined as $f\left(x\right)={\left(x-4\right)}^2+3$.

Step 6. define the function visually.

Using a graphing calculator or a graphing utility we construct the graph of the function $f\left(x\right)={\left(x-4\right)}^2+3$as shown:

Step 7. define the function numerically.

We are given that $f\left(x\right)={\left(x-4\right)}^2+3$, to find the numerical equivalent we must construct a table of values for this function as shown:

$x$	$f\left(x\right)={\left(x-4\right)}^2+3$
0 2 4 6	${\left(0-4\right)}^2+3=19$ width="101">2−42+3=7 ${\left(4-4\right)}^2+3=3$ ${\left(6-4\right)}^2+3=7$

Or

$x$	$f\left(x\right)$
0 2 4 6	19 7 3 7