Question

State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.

The range of the function$y=\sqrt{x}$is$\left\{y|>0\right\}$

Short answer

The given sentence is False.

The true sentence is The range of the function$y=\sqrt{x}$ is $\left\{y|\ge 0\right\}$.

Step-by-step solution

Step 1. Write the definition of range.

The range of a function is the set of values of dependent variable which is obtained by substituting the values of the independent variable for which the function is defined.

Step 2. Determine whether the given sentence is true or false.

The range of the function$y=\sqrt{x}$ is the set of values of y which is obtained by substituting the values of x for which the function is defined.

The graph of the function$y=\sqrt{x}$ is:

From the graph of the function $y=\sqrt{x}$,$y\ge 0$

Therefore, the range of the function$y=\sqrt{x}$ is $\left\{y|\ge 0\right\}$.

Therefore, the given sentence is false.

Step 3. Write the true sentence.

The true sentence is the range of the function$y=\sqrt{x}$ is $\left\{y|\ge 0\right\}$.