To find these values for the function f(x) = 4x² + 3x - 4, you simply need to substitute the given values into the function and perform the calculations. Here are the results:
(a) f(0):
f(0) = 4(0)² + 3(0) - 4
f(0) = 0 + 0 - 4
f(0) = -4
(b) f(4):
f(4) = 4(4)² + 3(4) - 4
f(4) = 4(16) + 12 - 4
f(4) = 64 + 12 - 4
f(4) = 72
(c) f(-4):
f(-4) = 4(-4)² + 3(-4) - 4
f(-4) = 4(16) - 12 - 4
f(-4) = 64 - 12 - 4
f(-4) = 48 - 4
f(-4) = 44
(d) f(-x):
f(-x) = 4(-x)² + 3(-x) - 4
f(-x) = 4x² - 3x - 4
(e) -f(x):
-f(x) = -(4x² + 3x - 4)
-f(x) = -4x² - 3x + 4
(f) f(x+3):
f(x+3) = 4(x+3)² + 3(x+3) - 4
f(x+3) = 4(x² + 6x + 9) + 3x + 9 - 4
f(x+3) = 4x² + 24x + 36 + 3x + 5
f(x+3) = 4x² + 27x + 41
(g) f(3x):
f(3x) = 4(3x)² + 3(3x) - 4
f(3x) = 4(9x²) + 9x - 4
f(3x) = 36x² + 9x - 4
(h) f(x+h):
f(x+h) = 4(x+h)² + 3(x+h) - 4
f(x+h) = 4(x² + 2xh + h²) + 3x + 3h - 4
f(x+h) = 4x² + 8xh + 4h² + 3x + 3h - 4
These are the values of the function for the given inputs and transformations.