Alice graphed *f(x)* and *g(x)*=*f*(*x*+1) on the same coordinate grid.

Which statement describes how the graphs of *f* and *g* are related?

A.The graph of the function *f(x)* is translated down 1 unit to produce *g(x)*.

B.The graph of the function *f(x)* is translated up 1 unit to produce *g(x)*.

C.The graph of the function *f(x)* is translated left 1 unit to produce *g(x)*.

D.The graph of the function *f(x)* is translated right 1 unit to produce *g(x)*.


The relationship between \( f(x) \) and \( g(x) = f(x + 1) \) involves a horizontal shift. Specifically, the function \( g(x) = f(x + 1) \) shifts the graph of \( f(x) \) **to the left** by 1 unit. 

This is because adding 1 inside the function (next to \( x \)) causes the graph to shift left, not right. To understand this, consider that \( g(x) \) takes the same output as \( f(x) \), but happens one unit earlier along the x-axis, which means every point is moved left.

Therefore, the correct answer is:

**C. The graph of the function \( f(x) \) is translated left 1 unit to produce \( g(x) \).**

Would you like more details on graph translations, or do you have any questions?

Here are some related questions to deepen your understanding:

1. What happens if the function is \( g(x) = f(x - 2) \)?
2. How does a vertical translation differ from a horizontal translation?
3. What does the graph of \( f(x - 3) \) look like in comparison to \( f(x) \)?
4. How would you describe the transformation for \( g(x) = f(x) + 4 \)?
5. If \( g(x) = -f(x) \), what kind of transformation occurs?

**Tip:** A transformation inside the parentheses of a function (affecting \( x \)) moves the graph horizontally, while a transformation outside moves it vertically.

Alice graphed f(x) and g(x) = f(x + 1) on the same coordinate grid. Which statement describes how the graphs of f and g are related?

Understand how the graph of f(x) translates to g(x) = f(x + 1) with a leftward shift of 1 unit. Explore the core algebraic concepts of function transformations and graph translations. Ideal for students in Grades 9-10.

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