Graphing Radical Functions: Domain and Range Insights

What happens to the graph of a radical function when a negative sign is placed in front of the radical?

• It reflects over the y-axis

• It reflects over the x-axis

• It shifts to the right

• No change occurs

Placing a negative sign inside the radical of a function causes the graph to:

• Reflect over the y-axis

• Shift upwards

• Shift downwards

• Reflect over the x-axis

For a function reflected over the y-axis and shifted up, in which quadrant will the graph primarily lie?

• Quadrant II

• Quadrant I

• Quadrant III

• Quadrant IV

When a radical function is reflected over the origin, what signs are associated with x and y?

• x is positive, y is negative

• x is negative, y is positive

• x is positive, y is positive

• x is negative, y is negative

What is the effect of placing a negative sign in front of the radical and inside it?

• Shifts the graph upwards

• Reflects the graph over the origin

• Reflects the graph over the x-axis

• Shifts the graph to the right

What is the effect of subtracting a number inside the radical of a function?

• Shifts the graph upwards

• Shifts the graph to the right

• Shifts the graph to the left

• Reflects the graph over the y-axis

What determines the new origin of a graph after it has been shifted?

• The coefficient of x

• The subtraction or addition inside the radical

• The reflection over the x or y-axis

• The multiplication factor outside the radical

How does adding a number inside the radical affect the graph of a radical function?

• Reflects it over the y-axis

• Shifts it to the left

• Shifts it to the right

• Reflects it over the x-axis

How does the graph of a radical function change when a positive number is added outside the radical?

• It shifts downwards

• It shifts to the left

• It shifts to the right

• It shifts upwards

What is the domain of a function that has been shifted 3 units to the right?

• x ≤ 3

• x > 3

• x < 3

• x ≥ 3