https://file.aiquickdraw.com/mathbot/file/1726725679601ie9cbs9g.jpg

The image shows a graph of a quadratic function with a downward-facing parabola and corresponding questions related to its domain, range, and other characteristics.

Here's a breakdown of the key points:
1. **Domain:** The domain of the function is "all real numbers." Since the graph of the parabola extends indefinitely left and right, the function is defined for every value of \( x \).
2. **Minimum \( y \)-value:** Based on the parabola, it appears that the minimum \( y \)-value is at \( y = 3 \), as highlighted on the graph where \( (1, 3) \) is shown as a point.
3. **Range:** The range of the function is "a subset of all real numbers." The lowest point is \( y = 3 \) and it opens downwards, so the function's values are all less than or equal to 3. Therefore, the correct range is \( y \leq 3 \).

The inequality provided for the range \( y \leq 3 \) should replace the incorrect \( y = 0 \).

### Do you have any other questions about this? I can also provide more details on:
1. How to calculate the domain and range for other types of functions.
2. How to find the vertex of a quadratic function from its equation.
3. Understanding how a parabola's direction (up or down) affects its minimum and maximum values.
4. Writing the equation of a parabola given its graph.
5. Determining intercepts (both x- and y-intercepts) from the graph of a function.

#### Tip: When dealing with quadratic functions, remember that if the parabola opens upwards, the vertex is the minimum point, and if it opens downwards, the vertex is the maximum point!

Identifying key characteristics of graphs of functions, including domain, range, and minimum/maximum values for a quadratic function.

Learn how to identify the domain, range, and minimum values of a quadratic function by analyzing its graph. This step-by-step solution explains how to interpret a downward-facing parabola, calculate the vertex, and define the function's range. Ideal for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation