Evaluate the functions

Given: f(x) = x³ - 3x and g(x) = x² - 8. What is f(10) - g(10)?


Solution:

Find the inverse of the matrix (if there is one) algebraically.

Find the inverse of the matrix (if there is one) algebraically.  If there isn’t an inverse, say that the matrix is singular

[3 1 2]

[3 2 -1]

[1 1 1]

Two chords intersect with the measures shown in the drawing.

What is the value of x?

Solution:

we know that the product of the lengths of one intersecting chord must be equal to the product of the lengths of the other, so...

For what value of x is if the lines are parallel in this figure?

Solution:

We know that x and 40.03 are supplementary, so x+40.03=180. Therefore x=139.97 degrees

What is the solution set for the given equation? 3|x + 4| = 18

Let's try a different approach this time...

3|x + 4| = 18

has the same solution as

|x + 4| = 6


We look for the number(s) that can add/subtract to obtain 6. We can see that x=2 will work. No other positive number will work, however if we consider negative numbers then -10 seems possible. In fact is does work because |-10+4| = |-6| = 6. So x=-10.

What is the number of turning points in the graph of the function of x defined below?

y = 2x² + 5x - 7

Solution:

The polynomial y has degree n=2 so the maximum number of turns it can have is n-1 = 2-1 = 1. (In fact we know that our polynomial is a quadratic and it opens upwards so this is another way to know it only has one turn).

Find x.

What is the value of x?

Solution:


TV is a diameter, and SU is perpendicular to TV. This means that x=8