Exploring Function Transformations and Shifts

The video tutorial on Desmos.com explores how to shift functions vertically and horizontally. It begins with a basic function, f(x) = x^2, and demonstrates vertical shifts by adding or subtracting constants. The tutorial then explains horizontal shifts by replacing x with x minus a constant. Using sliders for variables k and h, viewers can visualize these shifts. The concepts are generalized to other functions, including absolute value functions, encouraging viewers to experiment with these transformations on Desmos.

What is the primary goal of the video tutorial?

• To learn how to use Desmos for basic calculations.

• To explore how shifts in functions occur.

• To understand the history of graphing calculators.

• To solve complex algebraic equations.

How can you shift a function upwards?

• By dividing the function by a constant.

• By subtracting a constant from the function.

• By adding a constant to the function.

• By multiplying the function by a constant.

What happens to the graph of f(x) = x^2 when you subtract 3 from it?

• It shifts right by 3 units.

• It shifts up by 3 units.

• It shifts left by 3 units.

• It shifts down by 3 units.

What does the slider 'k' represent in the context of vertical shifts?

• The vertical shift of the graph.

• The slope of the graph.

• The x-intercept of the graph.

• The horizontal shift of the graph.

How do you shift a function to the right?

• By adding a constant to x.

• By subtracting a constant from x.

• By multiplying x by a constant.

• By dividing x by a constant.

What is the effect of replacing x with x - 1 in the function f(x) = x^2?

• The graph shifts 1 unit down.

• The graph shifts 1 unit to the left.

• The graph shifts 1 unit to the right.

• The graph shifts 1 unit up.

What happens to the vertex of the graph when you replace x with x + 5?

• It shifts 5 units to the right.

• It shifts 5 units to the left.

• It shifts 5 units up.

• It shifts 5 units down.

How would you write the function to shift the graph of f(x) = |x| to the left by 5 units?

• f(x) = |x| - 5

• f(x) = |x + 5|

• f(x) = |x| + 5

• f(x) = |x - 5|

What is the result of setting both h and k to zero in the function f(x) = (x - h)^2 + k?

• The graph remains at the origin.

• The graph shifts to the left.

• The graph shifts down.

• The graph shifts to the right.

What is encouraged at the end of the video?

• To solve algebraic equations manually.

• To read more about function shifts.

• To practice shifting functions on Desmos.

• To memorize the function shifts.