A box is to be constructed from a sheet of cardboard that

Question

1. A box is to be constructed from a sheet of cardboard that is 20 cm by 60 cm, by cutting out squares of length x by x from each corner and bending up the sides. What is the maximum volume this box could have?

2. Find the amplitude and period of y = -3cos(2x + 3).

Use your calculator to graph the function and state its symmetry.

Find the first positive x-intercept using your calculator's zero function.

3. Find two functions f(x) and g(x) such that f[g(x)] = x but g[f(x)] does not equal x.

4. State the vertical, horizontal asymptotes and zeros of the rational function, f(x) = x2+3x+2x2+5x+4.

Why is there no zero at x = -1?

5. Give an example and explain why a polynomial can have fewer x-intercepts than its number of roots.

Answer 1

There is an assessment that involves all intercept for calculator's zero function 1. A box is to be created from a sheet of cardboard that is 20 cm by 60 cm, by cutting out squares of length x by x from each corner and bending up the sides. What is the maximum volume this box could have? 2. Discover the amplitude and period of y = -3cos (2x + 3). Utilize your calculator to graph the function and state its symmetry. Discover the 1st positive x-intercept using your calculator's zero function. 3. Discover 2 functions f(x) and g(x) such that f[g(x)] = x but g[f(x)] doesn’t equal x. 4. State the vertical, horizontal asymptotes and zeros of the rational function, f(x) = x2+3x+2x2+5x+4. Why is there no zero at x = -1? 5. Provide an instance and illustrate why a polynomial can have fewer x-intercepts than its no of roots.