How does the graph of $$y = \sqrt{x}$$ change when we add a constant to x?

Adding a constant to x shifts the graph horizontally. For example, $$y = \sqrt{x - 2}$$ shifts the graph 2 units to the right.

What effect does subtracting a constant from a radical function have on its graph?

Subtracting a constant from the function shifts the graph downward. For example, $$y = \sqrt{x} - 3$$ shifts the graph down 3 units.

What is the effect of the transformation $$y = \sqrt{x + 4}$$ on the graph of $$y = \sqrt{x}$$ ?

This transformation shifts the graph 4 units to the left.

What is the significance of the endpoint in a radical function?

The endpoint (or vertex) is the lowest point on the graph of a square root function, indicating the minimum value.

How do you determine the vertex of a radical function in the form $$f(x) = \sqrt{x - h} + k$$ ?

The vertex is at the point (h, k).

What is the general form of a radical function?

The general form is $$f(x) = a\sqrt{x - h} + k$$ , where (h, k) is the vertex.

What happens to the graph of a radical function when 'a' is negative?

When 'a' is negative, the graph reflects over the x-axis.

How do you find the x-intercept of a radical function?

Set the function equal to zero and solve for x.

Practice Radical Functions Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

Back

The vertex is (-6, -3).

2.

FLASHCARD QUESTION

Front

Which equation shifts a radical function right 1 unit and up 2 units?

Back

3.

FLASHCARD QUESTION

Front

Match the equation with the graph: What is the equation for the graph that has a vertical shift up by 3?

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Match the equation with the graph: What is the equation for the graph that has a vertical shift down by 2?

Back

6.

FLASHCARD QUESTION

Front

What does the term 'radical function' refer to?

Back

A radical function is a function that contains a variable within a radical (square root, cube root, etc.).

7.

FLASHCARD QUESTION

Front

Back

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