Question

Identifying Linear Functions Determine whether the given function is linear. If the function is linear, express the function in the form $f\left(x\right)=ax+b$.

$f\left(x\right)=\sqrt{x}+1$

Short answer

The given function is not a linear function.

Step-by-step solution

Step 1. Definition of a linear equation and linear function.

In a linear equation the exponent of each variable is 1 and the variables may not be multiplied together. The graph of a linear equation is always a line.

In a linear function, each input value has a unique output value. In other words, for each point in domain, there is a unique value in the range of function. It can be written as $f\left(x\right)=mx+b$, where$m$ and$b$ are real numbers.

Step 2. Given information.

The given function is:

$f\left(x\right)=\sqrt{x}+1$

Step 3. Check whether the equation is linear or not.

The given function can be written as:

$f\left(x\right)=x^{\frac{1}{2}}+1$

The given function is not a linear function because the exponent of the variable$x$ is $\frac{1}{2}$.

Thus, the given function is not a linear function.