This video tutorial explores the similarities and differences between two functions, f(x) and g(x), focusing on horizontal and vertical translations. It explains how transformations affect linear equations, using f(x) = x as the basic function. The tutorial covers vertical translations affecting y-coordinates and horizontal translations affecting x-coordinates, with algebraic representations for each. It also discusses how to identify these transformations on a graph and through algebraic expressions, providing a comprehensive understanding of linear function transformations.

What is the basic linear function that serves as the foundation for all other linear functions?

• f(x) = 2x + 3

• f(x) = x^2

• f(x) = x

• f(x) = x - 5

How does a vertical translation affect the graph of a linear function?

• It rotates the graph.

• It reflects the graph over the x-axis.

• It changes the x-coordinates.

• It changes the y-coordinates.

If a function g(x) is vertically translated up by 4 units, what happens to its y-coordinates?

• They increase by 4.

• They decrease by 4.

• They are multiplied by 4.

• They remain the same.

What is the algebraic representation of a function with a slope of 2 and a y-intercept of -6?

• g(x) = -2x - 6

• g(x) = 2x + 6

• g(x) = -2x + 6

• g(x) = 2x - 6

How can you determine the horizontal translation of a function from its algebraic form?

• By looking at the y-intercept.

• By factoring out the greatest common factor.

• By checking the slope.

• By analyzing the x-coefficient.

What does a negative sign inside the parentheses of a function's algebraic form indicate about its horizontal shift?

• The graph shifts upwards.

• The graph shifts to the left.

• The graph shifts to the right.

• The graph does not shift.

In coordinate notation, how would you represent a horizontal translation of 3 units to the right?

• x, y → x, y - 3

• x, y → x, y + 3

• x, y → x + 3, y

• x, y → x - 3, y

What is the effect of a horizontal translation on the x-coordinates of a function?

• They remain unchanged.

• They are multiplied by a factor.

• They are shifted by a constant value.

• They are inverted.

If f(x) = 3x and g(x) = 3(x + 1), what is the horizontal translation from f(x) to g(x)?

• 2 units to the right

• 2 units to the left

• 1 unit to the left

• 1 unit to the right

What is the horizontal translation if the algebraic form of a function changes from f(x) = 3x to g(x) = 3(x - 1)?

• 3 units to the right

• 1 unit to the left

• 1 unit to the right

• 3 units to the left