given h(x) = x (sq. 2) + 5x - 6 over x + 6, find the value?

Question

1.) h (-4)

Answer 1

Function notation confuses some people... it's important to realize that, in this case, putting the x in parentheses doesn't indicate that you're multiplying it by h. It means that h is a function, and x is what we call the "dummy argument" -- the symbol that's used in the function definition.

If h(x) = (x² + 5x - 6)/(x + 6), then h is a function that takes an input value (which we're calling x) and applies that formula to it.

So h(-4) = [(-4)² + 5(-4) - 6] / [-4 + 6], which simplifies to (16 -20 - 6)/(2), or -10/2, which is -5.

Hope that helps!

P.S. Note to doug_donaghue: yeah, I was distracted. Fixed it, though. :)

Answer 2

Sherman81 spanked ya'll on this one. Lesson learned: Always simplify algebraically before evaluating an expression because it usually makes life easier (and less error-ridden).

Check this out...
h(x) = (x^2 + 5x - 6)/(x + 6) = x - 1, x ≠ -6

Instead of x, use whatever symbol you want.

h(☻) = ☻ - 1
h(☼) = ☼ - 1
h(♠) = ♠ - 1
h(♫) = ♫ - 1
h(-4) = -4 - 1 = -5

Therefore, when the variable, x, is -4, the function's value is -5. This could be written as the ordered pair (-4, -5). This ordered pair could be graphed on a piece of graph paper. With this point and several others (let x = -9, -8, -7, -5, -4, -3, -2, -1,…) one could see what the function, h, looks like. Give it a try. Find the following and graph:
h(-9) =
h(-8) =
h(-7) =
h(-6) = undefined...can't divide by zero!!
h(-5) =
h(-4) = ← we already did this one
h(-3) =
h(-2) =
h(-1) =

That hole in the graph at x = -6 will probably be something new to algebra students. Yes, the graph has a hole in it at x = -6. In other words, the graph is not continuous there. We call that a discontinuity for obvious reasons. Wow, this opens up lots and lots of new questions.

Answer 3

I'll rewrite what I think you are asking and then answer:

h(x) = (x^2 + 5x -6 ) / (x+6)

put x = -4 in place of x,

h(-4) = ((-4)^2 +5(-4) - 6 ) / ((-4) + 6)
h(-4) = (16 - 20 - 6)/ (2) = -10/2 = -5

Answer 4

h(x) = (x^2 + 5x - 6)/(x + 6)
h(x) = ((x + 6)(x - 1))/(x + 6)
h(x) = x - 1

h(-4) = -4 - 1
h(-4) = -4 + (-1)
h(-4) = -5

Answer 5

Jeeeezzzzzzz...... Jay H. I thought *I* was bad about dropping terms

Yeah, it's -5


Doug