Flashcard #6 (2nd Qtr) - ALG

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, from which other functions can be derived by transformations such as translations, reflections, and stretches.

Front

Describe the transformation of the function f(x) = x to g(x) = \frac{1}{4}x - 2.

Back

g(x) is less steep (due to the coefficient \frac{1}{4} which compresses the graph vertically) and translated down 2 units.

Front

How do you find the slope of a line given two points?

Back

The slope (m) is calculated using the formula m = \frac{y_2 - y_1}{x_2 - x_1}.

Front

What is the slope of a line perpendicular to another line with slope m?

Back

The slope of a line perpendicular to another line with slope m is -\frac{1}{m}.

Front

Rewrite the function f(x) = 2x - 2 if it is translated down 1 unit and the slope is reduced by 1/2.

Back

f(x) = x - 3.

Front

What is the value of y for the solution to the system of equations?

Back

The value of y is -\frac{11}{3}.

Front

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope.

Front

How do you determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a function to be 'steeper'?

Back

A function is 'steeper' when its slope is greater in absolute value, meaning it rises or falls more quickly.