Question

Consider the functions f(x)=3x^2+4 and g(x) = 2x-3 which of the statements about f + g are true select all that apply.

Answer 1

A and D

Explanation:

To find f + g, you can add both functions together, which results in the following:

`\displaystyle{\left(f+g\right)\left(x\right) = 3x^2+4+2x-3}\\\\\displaystyle{\left(f+g\right)\left(x\right) = 3x^2+2x+1}`

The domain is all real numbers is correct because you can substitute any x-values and have y-values.

The range of all real numbers is false because some x-values cannot be evaluated to a certain y-value. An example is when y = 0, no x-values satisfy the condition when y = 0.

It is a linear function is false because a linear function is defined as y = mx + b, only one-degree. However, the following function is second-degree, so it cannot be linear.

It is a quadratic function is correct because a quadratic function is defined as y = ax² + bx + c, the second-degree. Since the function has the highest degree of 2, thus, it is a quadratic function.