Alg Topic 10 Practice Test

Front

What is a translation in the context of functions?

Back

A translation is a transformation that shifts a graph horizontally, vertically, or both without changing its shape or orientation.

Front

How do you translate a function 2 units down and 5 units left?

Back

To translate a function 2 units down, subtract 2 from the function's output. To translate it 5 units left, replace x with (x + 5) in the function.

Front

What is the equation of the function g if f(x) = |x + 5| - 2 is translated 2 units down and 5 units left?

Back

g(x) = |x + 10| - 4.

Front

What does the equation y = √(x - 5) - 1 represent?

Back

This equation represents a square root function that is shifted right 5 units and down 1 unit.

Front

What is the slope of the graph of the inverse of the function f(x) = -\frac{1}{5}x - 2?

Back

The slope of the inverse function is the reciprocal of the original slope. Since the original slope is -\frac{1}{5}, the slope of the inverse is -5.

Front

How do you find the inverse of a function?

Back

To find the inverse of a function, swap the x and y variables and solve for y.

Front

What is the equation of the inverse function if f(x) = -\frac{1}{3}x - \frac{5}{3}?

Back

The inverse function is f^{-1}(x) = -3x - 5.

Front

What is the effect of a negative sign in front of a function?

Back

A negative sign in front of a function reflects the graph across the x-axis.

Front

What does shifting a function to the right mean?

Back

Shifting a function to the right means replacing x with (x - a), where a is the number of units to shift.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.