Graphing Radical Equations

Front

What is a radical equation?

Back

A radical equation is an equation in which a variable is contained within a radical (square root, cube root, etc.).

Front

What is the domain of a radical function?

Back

The domain of a radical function is the set of all possible input values (x) for which the function is defined, typically requiring the expression under the radical to be non-negative.

Front

What is the range of a radical function?

Back

The range of a radical function is the set of all possible output values (y) that the function can produce, often starting from a minimum value and extending to positive infinity.

Front

How do you find the domain of the function y = √(x) - 2?

Back

To find the domain, set the expression under the radical (x) to be greater than or equal to zero: x ≥ 0. Thus, the domain is [0, ∞).

Front

How do you find the range of the function y = √(x) - 2?

Back

The range can be found by determining the minimum value of the function. Since √(x) starts at 0, the minimum value of y is -2, so the range is [-2, ∞).

Front

What is the effect of the transformation y = √(x) + k on the graph of y = √(x)?

Back

The transformation y = √(x) + k shifts the graph vertically by k units. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What does the equation y = √(x + 1) + 2 represent in terms of transformations?

Back

This equation represents a horizontal shift to the left by 1 unit and a vertical shift upwards by 2 units from the parent function y = √(x).

Front

How do you determine the x-intercepts of a radical function?

Back

To find the x-intercepts, set the function equal to zero and solve for x. This gives the points where the graph crosses the x-axis.

Front

What is the significance of the vertex in the graph of a radical function?

Back

The vertex of a radical function is the point where the graph changes direction, often representing the minimum or maximum value of the function.

Front

What is the general form of a radical function?

Back

The general form of a radical function is y = a√(bx + c) + d, where a, b, c, and d are constants that affect the shape and position of the graph.