Q7. - Algebra 1

Question

State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.

An example of an exponential function is $y=3^x$.

Step-by-Step Solution

Answer

The sentence, “An example of an exponential function is $y=3^x$.  ” is true.

Step 1. Define the meaning of a function.

In mathematics, a function is a rule or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Step 2. Define an exponential function.

An exponential function is a function that can be described by an equation of the form $y=a{b}^x$ where, $a\ne 0,b>0$ and $b\ne 1$ .

Step 3. Check whether the given sentence is true or false.

Observe the function $y=3^x$.

This function is of the form $y=a{b}^x$, where, $a=1$ and $b=3$.

Since, $a\ne 0,b>0$ and $b\ne 1$.

So, the function $y=3^x$ is an example of an exponential function.

Therefore, the sentence, “An example of an exponential function is $y=3^x$.  ” is true.