Math Problem Statement

Consider the function, f(x) = 2x - 1. Use the above function to complete the following table.

Solution

The function provided is f(x)=2x−1f(x) = 2x - 1. We need to evaluate this function for each value of xx given in the table: x=1x = 1, x=0x = 0, x=−1x = -1, and x=2x = 2.

Let's go through each calculation:

  1. For x=1x = 1: f(1)=2(1)−1=2−1=1f(1) = 2(1) - 1 = 2 - 1 = 1

  2. For x=0x = 0: f(0)=2(0)−1=0−1=−1f(0) = 2(0) - 1 = 0 - 1 = -1

  3. For x=−1x = -1: f(−1)=2(−1)−1=−2−1=−3f(-1) = 2(-1) - 1 = -2 - 1 = -3

  4. For x=2x = 2: f(2)=2(2)−1=4−1=3f(2) = 2(2) - 1 = 4 - 1 = 3

So, the completed table is as follows:

\hline x & f(x) \\ \hline 1 & 1 \\ 0 & -1 \\ -1 & -3 \\ 2 & 3 \\ \hline \end{array}$$ Would you like further details on how I solved each part, or do you have any questions? ### Follow-Up Questions 1. What does the slope of this linear function represent? 2. How would the table change if the function was $$f(x) = -2x - 1$$? 3. What is the y-intercept of the function $$f(x) = 2x - 1$$, and how does it affect the graph? 4. How could you use this table to plot the graph of $$f(x) = 2x - 1$$? 5. How would the function change if we wanted it to be shifted up by 3 units? ### Tip For linear functions, the coefficient of $$x$$ represents the slope, which tells us the rate of change of $$f(x)$$ with respect to $$x$$.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Function Evaluation
Basic Algebra

Formulas

f(x) = 2x - 1

Theorems

None

Suitable Grade Level

Grades 6-8

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