Question

Identify each function as linear, quadratic, or exponential.

1. $y=3x^2$
2. $y=4{\left(3\right)}^x$
3. $y=2x+4$
4. $y=4{\left(0.2\right)}^x+1$

Short answer

1. $y=3x^2$ is a quadratic function.
2. $y=4{\left(3\right)}^x$ is an exponential function.
3. $y=2x+4$ is a linear function.
4. $y=4{\left(0.2\right)}^x+1$ is an exponential function.

Step-by-step solution

Step 1. Given Information.

Given to identify the type of functions given below is either linear, quadratic or exponential:

1. $y=3x^2$
2. $y=4{\left(3\right)}^x$
3. $y=2x+4$
4. $y=4{\left(0.2\right)}^x+1$

Step 2. Explanation.

A function is said to be linear if the degree of the function is 1 i.e., of the form $y=ax+b$

A function is said to be quadratic if the degree of the function is 2 i.e., of the form $y=a{x}^2+bx+c$

A function is said to be exponential is the variable is in the exponent i.e., of the form $y=a{b}^x+c$

For $y=3x^2$:

The function has 2 in the exponent i.e., the degree of the function is 2.

Hence the function is a quadratic function.

For $y=4{\left(3\right)}^x$:

The function has x in the exponent i.e., the degree of the function is a variable.

Hence the function is a exponential function.

For $y=2x+4$:

The function has 1 in the exponent i.e., the degree of the function is 1.

Hence the function is a linear function.

For $y=4{\left(0.2\right)}^x+1$:

The function has x in the exponent i.e., the degree of the function is a variable.

Hence the function is a exponential function.

Step 3. Conclusion.

Hence,

a.$y=3x^2$ is a quadratic function.

b.$y=4{\left(3\right)}^x$ is an exponential function.

c.$y=2x+4$ is a linear function.

d.$y=4{\left(0.2\right)}^x+1$ is an exponential function.