Question

(50 points) if anyone sees this can they help me out?

Classify each statement about the function f(x)=2x3+3 as true or false.

A) The domain of the function is all real numbers.
B) The range of the function is (−∞, 2).
C) The function has two x-intercepts.
D) The center of symmetry is (0, 3).



The function f(x)=(x−2)3 is transformed to g(x)=(x+1)3−2.

What transformations are performed from function f to function g?

A) Function f is translated to the left 2 units.
B) Function f is translated to the left 3 units.
C) Function f is translated up 1 units.
D) Function f is translated down 2 units.


The function f(x)=x+4−−−−√3 is transformed to f(x)=x−1−−−−√3+3.

What transformations are performed from function f to function g?

A) Function f is translated to the right 3 units.
B) Function f is translated down 1 unit.
C) Function f is translated to the right 5 units.
D) Function f is translated up 3 units


Graph this polynomial function by using its intercepts.
f(x)=x3+3x2−4x−12

Plot the points that represent the x- intercepts and y-intercept on the graph

Answer 1

See below for answers and explanations

Explanation:

Problem 1

• A is true because any real value of x will always produce a real value of y
• B is not true because it would contradict option A as explained previously
• C is not true because there is only one positive real root by Descartes' Rules of Signs, so there is only one real root and two imaginary roots
• D is true because the function is odd, so it is held that f(-x) = -f(x) which is true for the given function

Problem 2

• A is false
• B is true
• C is false
• D is true

Problem 3

I cannot read your problem

Problem 4

`f(x)=x^3+3x^2-4x-12\\0=x^3+3x^2-4x-12\\0=x^2(x+3)-4(x+3)\\0=(x^2-4)(x+3)\\0=(x-2)(x+2)(x+3)\\x_1=-3,\,x_2=-2,\,x_3=2`

Hence, the graph of the function would have points at (-3,0) (-2,0) and (2,0).

Answer 2

For the first part of the question, here is my classification of each statement:

A) True. The domain of the function is all real numbers.

B) False. The range of the function is all real numbers.

C) False. The function has no x-intercepts.

D) False. The center of symmetry is (0, 0).

For the second part, the transformations performed from function f to function g are:

A) Function f is translated to the left 3 units.

For the third part, the transformations performed from function f to function g are:

A) Function f is translated to the right 3 units.

B) Function f is translated up 3 units.

For the last part, you would need to find the x and y-intercepts of the polynomial function, and plot them on the graph. The x-intercepts can be found by setting x=0 in the equation and solving for y. The y-intercept can be found by setting y=0 and solving for x. Once the intercepts are found, you can plot them on the graph and connect them to form the graph of the polynomial function.