Math Problem Statement
Solution
The original function shown on the graph is . The modified function given in the problem is .
To analyze how this modification affects the graph, let's break down each part:
-
Horizontal Shift: The expression inside the logarithm shifts the graph horizontally. Specifically, it shifts the graph 5 units to the right, since subtracting a constant from inside a function moves the graph in the positive -direction.
-
Vertical Shift: The added outside the logarithmic function shifts the graph vertically. This shifts the graph 2 units up, as adding a constant to the function moves it in the positive -direction.
Therefore, the correct answers are:
- A: Move 5 spaces right.
- C: Move 2 spaces up.
Would you like more details or have any questions?
Related Questions:
- How would changing to affect the graph?
- What happens to the graph of if we change it to ?
- How does multiplying the logarithmic function by a constant (e.g., ) affect its graph?
- What transformation occurs if we add a negative constant outside the function, such as ?
- How would the graph of change if it was modified to ?
Tip:
When analyzing function transformations, remember that changes inside the function argument (like ) affect horizontal shifts, while changes outside (like ) affect vertical shifts.
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Math Problem Analysis
Mathematical Concepts
Logarithmic Functions
Transformations of Functions
Formulas
f(x) = log₂(x - h) + k
Theorems
Properties of logarithmic transformations
Suitable Grade Level
Grades 10-12
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