Suppose a function f (x) is defined by the given coordinates in the table below.
Determine the values A, B, C, and D in the table for the function g (x) = 2f (x) +5.

To solve this problem, we need to use the given function \( g(x) = 2f(x) + 5 \) and apply it to each coordinate point of \( f(x) \).

Let’s assume that the coordinates of \( f(x) \) are provided in a table like this:

\[
\begin{array}{c|c}
x & f(x) \\
\hline
x_1 & f(x_1) \\
x_2 & f(x_2) \\
x_3 & f(x_3) \\
x_4 & f(x_4) \\
\end{array}
\]

Then, the corresponding table for \( g(x) = 2f(x) + 5 \) will be:

\[
\begin{array}{c|c}
x & g(x) \\
\hline
x_1 & 2f(x_1) + 5 \\
x_2 & 2f(x_2) + 5 \\
x_3 & 2f(x_3) + 5 \\
x_4 & 2f(x_4) + 5 \\
\end{array}
\]

Given that \( g(x) \) can be represented as \( g(x) = 2f(x) + 5 \), we compute the values \( A \), \( B \), \( C \), and \( D \) as follows:

- \( A = 2f(x_1) + 5 \)
- \( B = 2f(x_2) + 5 \)
- \( C = 2f(x_3) + 5 \)
- \( D = 2f(x_4) + 5 \)

### Steps to determine the values \( A \), \( B \), \( C \), and \( D \):
1. Multiply each value of \( f(x) \) by 2.
2. Add 5 to each of the results obtained in step 1.

If the actual coordinates \( f(x_1), f(x_2), f(x_3), f(x_4) \) are known, you can directly compute \( A \), \( B \), \( C \), and \( D \).

Would you like to provide the specific values from the table, or do you need further details on any step? 

---

Here are 5 related questions to explore:
1. What happens to the graph of \( f(x) \) when transformed into \( g(x) = 2f(x) + 5 \)?
2. How would the function \( g(x) \) change if the transformation was \( g(x) = 3f(x) - 4 \)?
3. Can you determine \( g(x) \) given different function values for \( f(x) \)?
4. What effect does multiplying a function by a scalar have on its graph?
5. How does adding a constant to a function affect its graph?

**Tip:** Understanding how transformations affect functions graphically can help in quickly predicting the outcome of such changes.

Suppose a function f(x) is defined by the given coordinates in the table below. Determine the values A, B, C, and D in the table for the function g(x) = 2f(x) + 5.

Learn how to determine the values A, B, C, and D for the transformed function g(x) = 2f(x) + 5 using given coordinates. This problem explores function transformation concepts and applies the linear transformation theorem. Ideal for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation