Math Problem Statement
Solution
The graph shows the function and a transformed graph . The equation given is , indicating a vertical shift by units.
From the graph:
- The blue line represents .
- The red line represents .
To determine the value of , we compare the vertical shift between the two graphs. Both lines have the same slope (parallel), so the transformation is purely vertical. The red line is shifted upward from the blue line by comparing the y-intercepts. The y-intercept of is , while the y-intercept of is . Therefore, the vertical shift is 2 units up, meaning .
Thus, the correct choice is:
- k is equal to 2. The graph of is translated 2 unit(s) up compared to the graph of .
Would you like further details or have any questions?
Here are 5 related questions to expand your understanding:
- How do vertical shifts affect the equation of a function?
- How would the graph look if the shift was downward instead of upward?
- How does the slope of a line affect its transformations?
- What other types of transformations can be applied to a linear function?
- How can we find the value of if the transformation involved both a shift and a compression?
Tip: When transforming functions, vertical shifts affect the y-values but do not change the slope.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Graph transformations
Linear functions
Vertical shifts
Formulas
g(x) = f(x) + k
Theorems
Graph transformations theorem
Properties of linear functions
Suitable Grade Level
Grades 8-10
Related Recommendation
Find the Value of k for Transforming Line f to g: Algebraic Approach
Finding the Value of k in Function g(x) as a Transformation of f(x)
Vertical Shift of Functions: Solve for k in g(x) = f(x) + k
Finding the Horizontal Shift Value k for Function Transformation
Graph Transformations of f(x) = 2x + 1 with Horizontal Shifts