Math Problem Statement

Find the values of a, b, c, and d for the function g(x) = c * f(a * x - b) + d using the graph.

Solution

The equation provided in the image is g(x)=cf(axb)+dg(x) = c \cdot f(a \cdot x - b) + d. We are tasked with finding the values of aa, bb, cc, and dd based on the graph provided.

Looking at the graph:

  • The function has a horizontal step at y=2y = 2, and it jumps to y=4y = 4 at x=0x = 0, and then remains constant at y=4y = 4.

From this, we can deduce the following:

  1. Shift along the x-axis (b): The step occurs at x=0x = 0, so there doesn't seem to be any horizontal shift. Thus, b=0b = 0.

  2. **

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Transformations of functions
Piecewise functions

Formulas

g(x) = c * f(a * x - b) + d

Theorems

Transformation of functions
Shifts, scaling, and translation

Suitable Grade Level

Grades 10-12