Polynomials
Determine whether the following is a polynomial function. If it is a polynomial function, state its degree and leading coefficient.
f(x) = 4x-1 + 13
This function is not a polynomial!
What is the domain of the function?
f(x) = x2/5
(-∞, ∞)
If f(x) = 3(x+1)2 + 5, then what is the axis of symmetry of the graph of f?
x = -1
Describe what transformations have taken place on the following function from the base function of x3.
g(x) = 3(x-2)3
The function was shifted 2 to the right and stretched vertically by a factor of 3.
f(x) = x2 - 8x + 22
d(x) = x - 4
x - 4 + 6/(x-4)
Which of the following cannot be the number of nonreal zeros of a polynomial of degree 5 with real coefficients:
4, 0, 2, 3, or none of these?
3, because nonreal zeroes always come in pairs, so there cannot be an odd number of them.
What value of x is not in the domain of the function?
f(x) = 1/(x+4)
- 4
Determine if the function is a power function, given that c, g, k, π represent constants. If the function is a power function, state the power and constant of variation.
f(t) = -1/2 t5
The power is 5, and the constant of variation is -1/2
What is the y-intercept of the function?
g(x) = 3(x-2)3
(0,-24)
(x-7i)(x+7i)
x2 - 49
Let f(x) = (x+9)(x2+x-2) - 5. Which or the following statements is false?
a) x+9 is not a factor of f(x)
b) f(x) is not evenly divisible by x2+x-2
c) the remainder is -5 when f(x) is divided by x-6
c) is clearly false, because it names a factor that has nothing to do with the function.
Let f(x) = x2/(x+6).
Does this function have a vertical asymptote? Does it have a horizontal asymptote? Does it have a slant asymptote?
It has a vertical and slant asymptote but no horizontal asymptote.