Question

Consider$\mathit{y}\mathbf{=}{\mathit{x}}^{\mathbf{2}}\mathbf{-}\mathbf{7}\mathit{x}\mathbf{+}\mathbf{6}$. What are the domain and range?

Short answer

The domain is all real numbers. The range is all real numbers greater than or equal to the minimum value or $\mathbf{\{}\mathbf{y}\mathbf{/}\mathbf{y}\mathbf{\ge }\mathbf{-}\mathbf{6}\mathbf{.25}\mathbf{\}}$.

Step-by-step solution

Step 1. Define the concept.

The domain of a function is the complete set of possible values of the independent variable. The domain is the set of all possible $x$-values that will make the function "work" and will output real $y$-values.

Therangeof a function is the complete set of all possibleresulting valuesof the dependent variable ($y$,usually) after we have substituted the domain.

Step 2. Graphical representation of the quadratic function.

Draw the graph of the function: $y=x^2-7x+6$.

Step 3. State the domain and range of the function.

The function $y=x^2-7x+6$has the domain as all real numbers. The range is all real numbers greater than or equal to the minimum value. Since the function has a minimum value at $x=1.5$. Therefore, the range is $\{y|y\ge -6.25\}$.