Pre-calc FUNCTIONS--Evaluate the following f(x)=5x^2-4x for a.) f(3) b.) f(-2) c.)f(t-1) and d.) f(a+h)-f(a)?

Question

please explain what I have to do. If I have to use my calculator please tell me the keys you punched in. I have a TI-84plus which is very similar to the key strokes on the TI-83.
I need this answer/explanation soon since I have to turn in my work. Your help is greatly appreciated =)
Thanks a lot!

Answer 1

a. f(3)=5*3^2 -4*3 = 5*9 - 4*3 = 45-12 = 33
b. f(-2)=5*(-2)^2 -4*(-2) = 5*4 +4*2= 20+8 = 28
c. f(t-1)=5*(t-1)^2 -4*(t-1) = (t-1)*[5(t-1) -4] = (t-1)*(5t-5-4)=(t-1)*(5t-9) = 5t^2-14t+9
d. f(a+h)-f(a)=5*(a+h)^2-4*(a+h)-5*a^2+4a = 5(a^2+2ah+h^2)-4a-4h-5a^2+4a = 5a^2-5a^2+10ah+5h^2-4a+4a-4h= 10ah+5h^2-4h

Answer 2

There is no calculator for these problems.
The basic principle is to plug the value into the function.

For instance,

f(3) means plug in "3" for "x"

f(3) = 5(3)^2 - 4(3)
=5*9 - 12
=45 - 12
=33

b)
f(-2) = 5(-2)^2 - 4(-2)
=5*4 + 8
=20

c)
f(t - 1) = 5(t - 1)^2 - 4(t - 1)
=5(t^2 - 2t + 1) - 4t + 4
=5t^2 -10t + 5 - 4t + 4
=5t^2 - 14t + 9

d)For this one, you have to do two separate functions

f(a + h) = 5(a + h)^2 - 4(a + h)
= 5(a^2 + 2ah + h^2) - 4a - 4h
=5a^2 + 10ah + 5h^2 - 4a - 4h

f(a) = 5(a)^2 - 4(a)
=5a^2 - 4a

f(a + h) - f(a) =
[5a^2 + 10ah + 5h^2 - 4a - 4h] - [5a^2 - 4a]
=5a^2 + 10ah + 5h^2 - 4a - 4h - 5a^2 + 4a
=(5a^2 - 5a^2) + 10ah + 5h^2 + (4a - 4a) - 4h
=10ah + 5h^2 - 4h
=h(10a + 5h - 4)

Answer 3

f(x) = 5x^2 - 4x

f(3) = 5(3)^2 - 4(2)
f(3) = 5(9) - 8
f(3) = 45 - 8
f(3) = 37

f(-2) = 5(-2)^2 - 4(-2)
f(-2) = 5(4) + 8
f(-2) = 20 + 8
f(-2) = 28

f(t - 1) = 5(t - 1)^2 - 4(t - 1)
f(t - 1) = 5((t - 1)(t - 1)) - 4t + 4
f(t - 1) = 5(t^2 - 2t + 1) - 4t + 4
f(t - 1) = 5t^2 - 10t + 5 - 4t + 4
f(t - 1) = 5t^2 - 14t + 9

f(a + h) = 5(a + h)^2 - 4(a + h)
f(a + h) = 5((a + h)(a + h)) - 4a - 4h
f(a + h) = 5(a^2 + 2ah + h^2) - 4a - 4h
f(a + h) = 5a^2 + 10ah + 5h^2 - 4a - 4h
f(a) = 5a^2 - 4a
f(a + h) - f(a) = 5a^2 + 10ah + 5h^2 - 4a - 4h - (5a^2 - 4a)
f(a + h) - f(a) = 5a^2 + 10ah + 5h^2 - 4a - 4h - 5a^2 + 4a
f(a + h) - f(a) = 10ah + 5h^2 - 4h
f(a + h) - f(a) = 5h^2 - 10ah - 4h

Answer 4

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Answer 5

oh man, biiiiiiiiiiiig homework,

but i do only the last part

f(x)=5x^2-4x

a) f(3) = 5(3)^2-4(3) = 45 - 12 = ...

D) f(a+h)-f(a) = 5(a-h)^2-4(a-h) - [ 5a^2-4a ] = 5(a^2 + 2ah + h^2) - 4(a +h) - 5a^2 + 4a = 5a^2 + 10ah + 5h^2 - 4a - 4h - 5a^2 + 4a = 10ah + 5h^2 - 4h

check the answer with oterhs

Answer 6

f(x)= 5x*2-4x

f(3)= 5(3)*2 - 4(3)
= 5(9) - 12
= 45 - 12
= 33

f(-2)= 5(-2)*2 - 4(-2)
= 5(4) - (-8)
= 20 + 8
= 28

f(t-1)= 5(t-1)*2 - 4(t-1)
= 5(t-1)(t-1) - 4(t-1)
= 5(t*2 -2t + 1) - 4t+4
= (5t*2 - 10t + 5) -4t +4
SIMPLIFY = 5t*2 -14t + 9

I'm not really good at the last one... those always throw me off. sorry...