Understanding Function Shifts

The video tutorial explains how to shift a function, specifically a parabola, both horizontally and vertically. It begins by identifying the vertex as a key point for shifting. The function f(x) = x^2 is shifted to the right by three units and down by four units to form a new function G(x). The tutorial provides a step-by-step explanation of how to modify the equation to achieve these shifts, using x - 3 for the horizontal shift and subtracting 4 for the vertical shift. The video concludes with a visual verification of the shifts.

What is the primary focus when considering a shift in a parabola?

• The y-intercept

• The vertex

• The x-intercept

• The axis of symmetry

How do you mathematically represent a shift to the right by three units?

• Replace x with x + 3

• Replace x with x - 3

• Add 3 to the function

• Subtract 3 from the function

Why might replacing x with x-3 seem counterintuitive when shifting right?

• Because it decreases the x-coordinate

• Because it changes the function's shape

• Because it increases the y-coordinate

• Because it seems to shift left

What value do we want at x=3 after shifting the function?

• The same as when x=4

• The same as when x=2

• The same as when x=1

• The same as when x=0

What happens to the function's value at x=4 after shifting right by three?

• It becomes 3

• It becomes 2

• It becomes 1

• It becomes 0

What is the next step after shifting the function to the right?

• Shift up by four

• Shift down by four

• Shift left by four

• Shift right by four

How do you adjust the function to shift it down by four units?

• Subtract 4 from the function

• Add 4 to the function

• Divide the function by 4

• Multiply the function by 4

What is the final equation for G(x) after all shifts?

• G(x) = (x + 3)^2 + 4

• G(x) = (x - 3)^2 - 4

• G(x) = (x - 3)^2 + 4

• G(x) = (x + 3)^2 - 4

What effect does replacing x with x+3 have on the function?

• Shifts the function left by three

• Shifts the function down by three

• Shifts the function right by three

• Shifts the function up by three

What is the purpose of subtracting 4 from the function?

• To shift the function down

• To shift the function up

• To shift the function left

• To shift the function right