Math Problem Statement

Given the graph of the function f, answer the following questions about its values at specific points and complete the table with the function's values at other points.

Solution

The image shows a graph of a quadratic function ff and several related questions in Dutch.

a) Fill in the following:

  • f(3)=f(3) =
  • f(1)=f(-1) =
  • f(1)=f(1) =
  • f(_)=2f(\_ ) = -2

From the graph:

  1. To find f(3)f(3), look at where x=3x = 3 intersects the graph. This point corresponds to f(3)=2f(3) = 2.
  2. For f(1)f(-1), check the point where x=1x = -1 intersects the graph, which gives f(1)=2f(-1) = 2.
  3. For f(1)f(1), find the intersection at x=1x = 1, which shows f(1)=0f(1) = 0.
  4. To find f(x)=2f(x) = -2, look for the value of xx where the graph is at y=2y = -2. This occurs at x=2x = 2.

So, the answers for part (a) are:

  • f(3)=2f(3) = 2
  • f(1)=2f(-1) = 2
  • f(1)=0f(1) = 0
  • f(2)=2f(2) = -2

b) Complete the table:

  • For x=1x = -1, f(1)=2f(-1) = 2 (from the graph).
  • For x=4x = 4, check the intersection at x=4x = 4 on the graph, which gives f(4)=7f(4) = 7.

Thus, the completed table for part (b) is: [ \begin{array}{c|c|c} x & f(x) \ \hline -1

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Math Problem Analysis

Mathematical Concepts

Graph of a function
Quadratic functions
Function evaluation

Formulas

f(x) = ax^2 + bx + c

Theorems

Graph of a quadratic function

Suitable Grade Level

Grades 8-10