Question

Write an equation to math each graph

Answer 1

f(x) = -|x +1| + 1

Explanation:

To determine the function of an absolute value graph, you can follow these steps:

Step 1: Identify the general shape of the graph.

Look at the graph and observe its overall shape. Absolute value functions typically have a V-shape, where the graph is symmetric with respect to the vertical axis.

Step 2: Locate key points on the graph.

Identify and note down the coordinates of any key points on the graph, such as the vertex (lowest or highest point on the graph) and any x-intercepts (where the graph intersects the x-axis).

Step 3: Write the general form of an absolute value function.

The general form of an absolute value function is:

→ f(x) = a |x - h| + k

where:

• a is the vertical stretch or compression factor.

• h is the horizontal shift (the x-coordinate of the vertex).

• k is the vertical shift (the y-coordinate of the vertex).

Step 4: Determine the values of a, h, and k.

Using the information obtained from Step 2, you can now determine the specific values of a, h, and k for the given absolute value function.

• a: The value of a is equal to the vertical distance from the vertex to any of the x-intercepts. If the graph opens upwards (V-shape), a is positive; if it opens downwards (A-shape), a is negative.
• h: The value of h is the x-coordinate of the vertex, which you can obtain directly from the graph.
• k: The value of k is the y-coordinate of the vertex, which can also be read from the graph.

Step 5: Write the specific function.

Now that you have determined the values of a, h, and k, you can write the specific function of the absolute value graph.

Keep in mind that depending on the complexity of the graph, it may be challenging to read the exact coordinates of the vertex and x-intercepts from the graph. In such cases, you might need additional information or data points to determine the function accurately. Luckily in our case, we can locate points easily.
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The given graph is an absolute value function. Where:

• a = -1
• h = -1
• k = 1

Substituting these values into the general form of an absolute value function:

⇒ f(x) = a |x - h| + k

⇒ f(x) = (-1) |x - (-1)| + 1

∴ f(x) = -|x +1| + 1

Therefore, the given question is solved. we can check our answer using a graphing calculator.