Question

I have a graph with points negative 2, -4 -1, -1 0, 2 1, 5 what value of k would create the function y equals f of KX on the graph if it's transformed version of the function f of x equals x + 2

Answer 1

To find the appropriate value of \( k \) that transforms the function \( f(x) = x + 2 \) into \( y = f(kx) \), we need to understand how the transformation affects the graph.

1. **Identify the Original Function**: The function given is \( f(x) = x + 2 \).

2. **Transformation**: The function \( y = f(kx) \) can be rewritten as:
\[
y = kx + 2
\]
In this transformation, the slope of the line (which corresponds to the value of \( k \)) determines how steep the line becomes.

3. **Analyzing the Points**: You provided the following points:
- (-2, -4)
- (-1, -1)
- (0, 2)
- (1, 5)

4. **Finding the Slope from Points**: To find the multiplier \( k \), we'll calculate the slope of the transformed function using selected points \( (x_1, y_1) \) and \( (x_2, y_2) \):
- From the points \( (0, 2) \) and \( (1, 5) \), the slope \( m \) can be calculated as:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 2}{1 - 0} = \frac{3}{1} = 3
\]

5. **Setting the Slope**: In our transformed function \( y = kx + 2 \), the slope \( k \) would need to equal the calculated slope:
\[
k = 3
\]

Therefore, the value of \( k \) that transforms \( f(x) = x + 2 \) into a function whose graph includes the provided points is \( k = 3 \).