Chapter 13, Problem 1RE

Evaluating a FunctionIn Exercises 1 and 2, evaluate the function at the given values of the independent variables. Simplify the results.

$f(x,y)=x^{2}y-3$

(a) $f(0,4)$

(b) $f(2,-1)$

(c) $f(-3,2)$

(d) $f(x,7)$

To determine

To calculate: The function is, $f\left(x,y\right)=x^{2}y-3$ and the point is $\left(0,4\right)$ is given find the value of the provided function where $f\left(x,y\right)=x^{2}y-3$

Answer to Problem 1RE

Solution:

The value is, $-3$.

Explanation of Solution

Given:

The function is, $f\left(x,y\right)=x^{2}y-3$ and the point is $\left(0,4\right)$.

Formula used: Given a function f(x, y) = xy then f(a, b) = ab where a, b belongs to the set of whole numbers

Calculation:

Put the values as $x=0,y=4$

$\begin{array}{c}f\left(0,4\right)=x^{2}y-3\\ =0^2\times 4-3\\ =-3\end{array}$

To determine

To calculate: The function is, $f\left(x,y\right)=x^{2}y-3$ and the point is $\left(2,,-1\right)$.

Is given, find the value of the provided function where $f\left(x,y\right)=x^{2}y-3$

Answer to Problem 1RE

Solution:

The value is, $-7$.

Explanation of Solution

Given:

The function is, $f\left(x,y\right)=x^{2}y-3$ and the point is $\left(2,,-1\right)$.

Formula used: Given a function f(x, y) = xy then f(a, b) = ab where a, b belongs to the set of whole numbers

Calculation:

Put the values as $x=2,y=-1$

$\begin{array}{c}f\left(2,-1\right)=x^{2}y-3\\ =2^2\times \left(-1\right)-3\\ =-4-3\\ =-7\end{array}$

To determine

To calculate: The function is, $f\left(x,y\right)=x^{2}y-3$ and the point is $\left(-3,2\right)$.

Is given, find the value of the provided function where $f\left(x,y\right)=x^{2}y-3$

Answer to Problem 1RE

Solution:

The value is, $15$.

Explanation of Solution

Given:

The function is, $f\left(x,y\right)=x^{2}y-3$ and the point is $\left(-3,2\right)$.

Formula used: Given a function f(x, y) = xy then f(a, b) = ab where a, b belongs to the set of whole numbers

Calculation:

Put $x=-3,y=2$

$\begin{array}{c}f\left(-3,2\right)=x^{2}y-3\\ ={\left(-3\right)}^2\times 2-3\\ =18-3\\ =15\end{array}$

To determine

To calculate: The function is, $f\left(x,y\right)=x^{2}y-3$ and the point $\left(x,7\right)$.

Is given, find the value of the provided function where $f\left(x,y\right)=x^{2}y-3$

Answer to Problem 1RE

Solution:

The value is, $7x^2-3$.

Explanation of Solution

Given:

The function is, $f\left(x,y\right)=x^{2}y-3$ and the point $\left(x,7\right)$.

Formula used: Given a function f(x, y) = xy then f(a, b) = ab where a, b belongs to the set of whole numbers

Calculation:

Put $x=x,y=7$

$\begin{array}{c}f\left(x,7\right)=x^{2}y-3\\ =x^2\times 7-3\\ =7x^2-3\end{array}$