Transformations of Radical Functions

What does it mean to reflect a function over the y-axis?

• It means that for every point (x, y) on the graph, the point (-x, y) will also be on the graph. This changes the sign of the input.

• It means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph. This changes the sign of the output.

• It means that the function is shifted to the right by a certain value.

• It means that the function is stretched vertically by a factor of two.

What is a radical function?

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

• A function that is defined by a polynomial equation.

• A function that has a constant value regardless of the input.

• A function that only includes integer values.

What is the transformation of the function @@g(x) = ext{sqrt}(x - 3) + 2@@ compared to the parent function?

• The function is translated left by 3 units and down by 2 units compared to the parent function @@f(x) = ext{sqrt}(x)@@.

• The function is translated right by 3 units and down by 2 units compared to the parent function @@f(x) = ext{sqrt}(x)@@.

• The function is translated right by 3 units and up by 2 units compared to the parent function @@f(x) = ext{sqrt}(x)@@.

• The function is reflected over the x-axis compared to the parent function @@f(x) = ext{sqrt}(x)@@.

What does it mean to reflect a function over the x-axis?

• For every point (x, y) on the graph, the point (x, -y) will also be on the graph. This changes the sign of the output.

• For every point (x, y) on the graph, the point (-x, y) will also be on the graph. This changes the sign of the input.

• For every point (x, y) on the graph, the point (x, y) will remain unchanged. This keeps the output the same.

• For every point (x, y) on the graph, the point (-x, -y) will also be on the graph. This reflects the function over the origin.

What is the effect of a horizontal shift on the graph of a function?

• A horizontal shift moves the graph left or right. A shift left by 'h' units is represented by replacing 'x' with 'x + h', while a shift right by 'h' units is represented by replacing 'x' with 'x - h'.

• A horizontal shift stretches the graph vertically.

• A horizontal shift reflects the graph across the x-axis.

• A horizontal shift changes the slope of the graph.

How do you identify transformations from the equation of a radical function?

• By comparing the function's equation to the parent function and looking for shifts, stretches, and reflections.

• By analyzing the degree of the radical and determining the domain.

• By finding the zeros of the function and plotting them on a graph.

• By simplifying the radical expression to its lowest terms.

What does it mean to translate a function right by 'h' units?

• Translating a function right by 'h' units means replacing 'x' with 'x + h' in the function's equation.

• Translating a function right by 'h' units means replacing 'x' with 'x - h' in the function's equation.

• Translating a function right by 'h' units means adding 'h' to the function's output.

• Translating a function right by 'h' units means multiplying the function's output by 'h'.

What is a vertical stretch in the context of functions?

• A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

• A vertical stretch occurs when the input values of a function are multiplied by a factor greater than 1, making the graph wider.

• A vertical stretch occurs when the output values of a function are added to a constant, shifting the graph upwards.

• A vertical stretch occurs when the function is reflected over the x-axis.

How does shifting a function down affect its equation?

• Shifting a function down by 'k' units involves adding 'k' to the function's output.

• Shifting a function down by 'k' units involves multiplying the function's output by 'k'.

• Shifting a function down by 'k' units involves subtracting 'k' from the function's output. For example, shifting @@f(x) = ext{sqrt}(x)@@ down by 3 gives @@g(x) = ext{sqrt}(x) - 3@@.

• Shifting a function down by 'k' units involves dividing the function's output by 'k'.

How do you determine the domain of a radical function?

• The domain is determined by the values of x that make the expression under the radical non-negative.

• The domain is all real numbers.

• The domain is determined by the values of x that make the expression under the radical positive only.

• The domain is determined by the values of x that make the expression under the radical negative.