Math Problem Statement

Using the graph, find p(0)p(0)and find xxsuch that p(x)=−2.p(x)=−2.

Using the graph, find p(0) and find x such that p(x) = -2.

Solution

From the graph, we need to extract two pieces of information:

  1. Finding p(0)p(0): This represents the value of the function p(x)p(x) when x=0x = 0. To find this, we look at where the graph intersects the y-axis (because x=0x = 0 on the y-axis).

    From the graph, at x=0x = 0, the red curve crosses the y-axis at y=1y = 1. Hence, p(0)=1p(0) = 1.

  2. Finding xx such that p(x)=2p(x) = -2: Here, we need to find the value of xx where the graph intersects y=2y = -2.

    Looking at the graph, the red curve crosses the horizontal line y=2y = -2 when x5x \approx -5.

So, the answers are:

  • p(0)=1p(0) = 1
  • p(x)=2p(x) = -2 when x=5x = -5

Do you want more details or have any questions?

Here are 5 related questions you might explore:

  1. What is the general shape of the graph of a cubic function?
  2. How do you find the roots of a function from its graph?
  3. What is the significance of the x-intercept on a graph?
  4. Can a function have more than one value for p(x)=2p(x) = -2?
  5. How can you estimate the value of a function at non-integer points?

Tip: Always double-check both the x- and y-values carefully when reading from a graph to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Graph Interpretation
Function Evaluation

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8