Question

The graph of a quadratic function with vertex (4, 1) is shown in the figure below.
Find the domain and the range.

Answer 1

Answer:

Domain: All reals

Range: y < 1 OR 1 > y

Step-by-step explanation:

Domain is all the x values the line passes through.

Range is all the y values the line passes through.

Every parabola has a domain of all real numbers since they all stretch out to infinity on the x axis.

This parabola stops going up at y = 1, so the range is all real numbers below 1, which is either y < 1 or 1 > y.

Answer 2

The domain of the given quadratic function is all reals and the range is $y\leq 1$.

Given:

• The graph of a quadratic function.

• The vertex of the quadratic function is $(4,1)$.

To find:

The domain and range of the given function.

Explanation:

The set of all input values is known as domain and the set of all output values is known as range.

The given function is defined for all real values of $x$. So, the domain of the given function is all real numbers.

From the given graph, it is clear that the maximum output value of the function is $1$. So, the possible output values are $y\leq 1$.  

Therefore, the domain of the given quadratic function is all reals and the range is $y\leq 1$.

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