...I know my title isn't very descriptive, but there are 3 types of questions i'm in the need of help for. I am very appreciative for any help!
Write the following absolute value expressions as piecewise expressions.
1. |x^2 + x - 12|
I know that it's possible to graph it using my calculator, but is there a way not to use my calculator? Half of calculus is without calculator.
you should already know what y = x^2 + x - 12 looks like ... well, y = |x^2 + x - 12| is the same graph except that the part that is below the x-axis (negative) is reflected to the positive side.
y = x^2 + x - 12 , x < -4 or x > 3
y = -(x^2 + x - 12) , -4 < x < 3
Solve the following by factoring and making the appropriate sign charts. Write your solutions in interval notation.
2. x^2 - 16 > 0
I got (4, ∞) but I don't know what a sign chart is.
x^2 - 16 > 0 ... note that x^2 - 16 = 0 at x = + 4 and x = -4
plot these two numbers on a number line ... it breaks the number line into three sections ...
x < -4 , -4 < x < 4 , and x > 4
take any number in each interval, and "test" it in the original inequality ... if it makes the inequality true, then all values of x in that interval make the inequality true.
you'll see that you forgot the interval (-∞ , -4)
3. x^2 + 12x + 36 - 9y^2
start with this ... (x + 6)^2 - (3y)^2