How do I know if f(x)=-7x+4 when x=-4 is greater than f(x)= -7x+4 when x= -5 or is it less than or equal to?
2006-09-30 06:10:08 · 8 answers · asked by mxyzbq 1 in Science & Mathematics ➔ Mathematics
when I plug it in, it looks like this:
f(-4)= 32 and f(-5)=39 so what do I do from there?
2006-09-30 06:14:22 · update #1
then Do I simplify or something?
2006-09-30 06:15:34 · update #2
Probably you've made the same mistake I made at first: that the equation depends on x, so the greater x is, the greater the result becomes. But such logic is meaningless. First we have to know what kind of function f(x) is (decreasing ,increasing or constant), and then judge about the way x will affect the equation.
If you notice f(x)= -7x+4 carefully, you see that it's a decreasing function (you can draw it to understand better-- it's a line with tangant value of -7 which interrupts x axis in (-4,0) ). In a decreasing function we have: x>x' -> f(x)
x=-4 > x'=-5 -> f(x)=f(-4)=32 < f(x')=f(-5)=39
2006-09-30 07:12:04 · answer #1 · answered by Anonymous · 0⤊ 0⤋
You could just substitute the respective values of x and prove it. Or you can look at the slope of the equation, which is -7. As a negative number, it means the line will slant up to the left. Since x=-4 is farther right than x=-5, that means than the f(x) when x=-4 will be less than f(x) when x=-5
2006-09-30 06:15:44 · answer #2 · answered by MateoFalcone 4 · 0⤊ 0⤋
its because the 7 in -7x + 4 is negative and your x value is also negative, so the negative numbers cancel out. So although -5 is less than -4, f(-5) is greater than f(-4).
2006-09-30 06:21:20 · answer #3 · answered by Sherman81 6 · 0⤊ 0⤋
You can just do the substitution
f(-4)=-7(-4)+4=32
f(-5)=-7(-5)+4=39
Without actualy doing the calculations, you can just look at the slope, -7 in the case. since the slope is<0, when x decreases y increases & vice versa. If the slope were >0, when x increased, y would increase & vice versa.
Since -5 <-4, x has decreased therefore y increases.
2006-09-30 09:32:49 · answer #4 · answered by yupchagee 7 · 0⤊ 0⤋
substitue the value of x
i) f(-4) = -7 * -4 + 4
= 28 + 4
= 32
ii) f(-5) = -7 * -5 + 4
= 35 + 4
= 39
so from i and ii
32 < 39
so f(-4) < f(-5)
2006-09-30 06:17:45 · answer #5 · answered by the brillant once! 2 · 0⤊ 0⤋
u know some calculus
just find dy/dx = -7
so it is an decreasing function
therefore
f(x) decreases as x inxreases hence f(-5)>f(-4)
2006-09-30 06:19:55 · answer #6 · answered by Gunjit M 2 · 0⤊ 0⤋
You plug in x to each equation then see if the statement is true.
2006-09-30 06:12:07 · answer #7 · answered by Liz 2 · 0⤊ 0⤋
f(-4)= 32 and f(-5)=39
32 is less than 39
f(-4) is less than f(-5)
2006-09-30 07:09:00 · answer #8 · answered by horse 2 · 0⤊ 0⤋