Absolute Value Study Material

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

What does the graph of an absolute value function typically look like?

Back

The graph of an absolute value function is a V-shape, with a vertex at the point where the expression inside the absolute value equals zero.

Front

How does the coefficient in front of an absolute value function affect its graph?

Back

A positive coefficient stretches the graph vertically, while a negative coefficient reflects it across the x-axis.

Front

What is the vertex form of an absolute value function?

Back

The vertex form of an absolute value function is given by f(x) = a|x - h| + k, where (h, k) is the vertex.

Front

How do you find the vertex of the function f(x) = -3|-x + 1| + 4?

Back

The vertex can be found by identifying the point (h, k) from the vertex form. Here, h = -1 and k = 4, so the vertex is (-1, 4).

Front

What is the solution to the equation |x + 5| = 9?

Back

The solutions are x + 5 = 9 or x + 5 = -9, leading to x = 4 or x = -14.

Front

What does it mean if an absolute value equation has no solution?

Back

An absolute value equation has no solution if the expression inside the absolute value cannot equal a negative number.

Front

How do you solve the equation 2|x - 4| + 8 = 18?

Back

First, isolate the absolute value: 2|x - 4| = 10. Then divide by 2: |x - 4| = 5. Solve for x to get x = 9 and x = -1.

Front

What is the domain of the function f(t) = -2|t - 15| + 50?

Back

The domain is the set of all possible values for t, which in this case is 0 ≤ t ≤ 40.

Front

True or False: The absolute value of a negative number is always positive.

Back

True. The absolute value of any number, whether negative or positive, is always non-negative.