Q45. - Algebra 1

Question

EDUCATION The average national math test scores $f\left(t\right)$ for 17-year-olds can be represented as a function of the national science scores $t$ by $f\left(t\right)=0.8t+72$.

a. Graph this function.

b. What is the science score that corresponds to a math score of 308 ?

c. What is the domain and range of this function?

Step-by-Step Solution

Answer

a. The required graph of the function   is as follows.

 

b. 295 is the science score that corresponds to the math score of 308.

c. The domain is the set of science score i.e. $\left\{295\right\}$ and the range is set of math score i.e. $\left\{308\right\}$.

Part a. Step 1. Given.

The function is given as $f\left(t\right)=0.8t+72$.

Part a. Step 2. Graph.

The graph of the given function $f\left(t\right)=0.8t+72$ will be as follows.

Part a. Step 3. Interpretation.

The line in the required graph passes through the points $\left(-90,0\right)$ and $\left(0,72\right)$.

Part b. Step 1. Given.

The given function is $f\left(t\right)=0.8t+72$ and math score is 3058.

Part b. Step 2. Calculation.

Substitute 308 for $f\left(t\right)$ in the given function.

  $\begin{array}{c}308=0.8t+72\\ 0.8t=308-72\\ t=\frac{236}{0.8}\\ =295\end{array}$

Hence, the science score is 295.

Part b. Step 3. Conclusion.

The relation between the math score and science score being the given function gives the value of the science score when the math score is given.

Part c. Step 1. Given.

 $f\left(t\right)=0.8t+72$ is the given function.

Part c. Step 2. Calculation.

The values of $t$ will be the domain and the values of  $f\left(t\right)$ will be the range of the given function.

The domain is the set of science scores which is $\left\{295\right\}$ and the range is the set of math scores which is $\left\{308\right\}$.

Part c. Step 3. Conclusion.

Thus in conclusion the domain and range of the given function are singleton sets.