Question

A function is given algebraically by the formula

$f\left(x\right)={\left(x-4\right)}^2+3$. Complete these other ways to represent f:

(a) Verbal: “Subtract 4, then ___ and ___.

(b) Numerical:

Short answer

(a) The function definition is from x “subtract 4 and square it and add three”

(b) The value are:

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

Step-by-step solution

Part a. Step 1. Use the definition of functions.

Function, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

A function is also 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: $X\to Y$.

Part a. Step 2. analyze the given information.

We are given that $f\left(x\right)={\left(x-4\right)}^2+3$, here 4 is subtracted from the variablexand then result is squared and lastly 3 is being added.

Part a. Step 3. define the function in words.

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

Part b. Step 1. Use the definition of functions.

Function, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

A function is also 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: $X\to Y$.

Part b. Step 2. analyze the given information.

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.

Part b. Step 3. find the value by plugging x-values.

We are given that $f\left(x\right)={\left(x-4\right)}^2+3$, to find we value of the function as shown:

$x$	$f\left(x\right)={\left(x-4\right)}^2+3$
0 2 4 6	$\left(0-4\right)2+3=19$ ${\left(2-4\right)}^2+3=7$ ${\left(4-4\right)}^2+3=3$ ${\left(6-4\right)}^2+3=7$