Function Translations Practice Flashcard

Front

What is the DOMAIN of the function represented by the graph?

Back

The DOMAIN is the set of all possible x-values for which the function is defined. For the given graph, the DOMAIN is -4 ≤ x ≤ 3.

Front

Describe the transformations that map y = g(x) to y = -g(x + 6).

Back

The transformations include reflecting over the x-axis and shifting left 6 units.

Front

What transformations are applied to the graph of y = (x - 3)^3 - 2?

Back

The graph is shifted right 3 units and down 2 units.

Front

How would you describe the behavior of a function on the domain interval (-1, 1) if it is constant?

Back

The function does not change its value; it remains the same throughout the interval.

Front

Find the equation of the function y=x^2 that has moved 8 units down and reflected across the y-axis.

Back

The equation is y=(-x)^2-8.

Front

What does it mean for a function to be increasing on an interval?

Back

A function is increasing on an interval if, as x increases, the value of the function also increases.

Front

What does it mean for a function to be decreasing on an interval?

Back

A function is decreasing on an interval if, as x increases, the value of the function decreases.

Front

What is a reflection of a graph across the x-axis?

Back

A reflection across the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What is a reflection of a graph across the y-axis?

Back

A reflection across the y-axis means that for every point (x, y) on the graph, the point (-x, y) will also be on the graph.

Front

What is the effect of shifting a graph left by 6 units?

Back

Shifting a graph left by 6 units means that every point on the graph moves 6 units to the left along the x-axis.