In this question, we'll gather information for sketching the function f(x) = 1 = ( 12/14+7) 13. Ꮖ 1. For which values of x is f(x) continuous? f(x) is continuous for x in the interval (0, Inf) U(-Inf, 0) 2. Where does this function cross the x-axis? If there is more than one answer, enter a list of numbers; if there are no answers, enter none. x = -3 3. Does f(x) have any horizontal asymptotes? If there is more than one answer, enter a list of numbers; if there are no answers, enter none. Horizontal asymptote(s) at y = 7^(1/3) 4. Does f(x) have any vertical asymptotes? If there is more than one answer, enter a list of numbers; if there are no answers, enter none. Vertical asymptote(s) at x = 0 5. Find the first derivative of f(x). f'(x) = 1/3 (21/x+7)^(-2/3)*(-(21)/(x^(2))) 6. Give all values of x for which f'(x) exists and is negative. If there are none, write none. f'(x) <0 for x in (-0,0)(0,∞) 7. Give all values of x for which f'(x) exists and is positive. If there are none, write none. f'(x) > 0 for x in none 8. What is the best description of the curve y = it exists and has a vertical tangent line f(x) at x = -3? 9. What is the best description of the curve y = f(x) at x=0? it has an infinite discontinuity 10. Combine all of your answers to make a detailed sketch of y = f(x). Your sketch should include: ⚫ correct locations for all discontinuties, intercepts, and asymptotes; • labels of any x-values where the function's derivative is 0 or undefined, with the appropriate behaviour sketched; • correct intervals of increase and decrease. Your graph does not have to include labelled inflection points.

How do you find the domain for the composition of two functions, fg ?

Why do we restrict the domain of the function f(x)=x2 to find the function's inverse?

What is the composition of two functions, fg ?

Use a calculator to evaluate fx=8x at x=2.

Use your schools library, the Internet, or some other reference source to find real-life applications of approximations of functions.

How do the graphs of the functions f(x)=x2 and f(x)=x21 differ? We graphed them at the start of this section. What is the difference between their graphs? How are their graphs the same?

How can you determine whether a function is odd or even from the formula of the function?

To graph the function f, we plot the points (x,) in a coordinate plane. To graph f(x)=x22, we plot the points (x,). So the point (3,) is on the graph of f. The height of the graph of f above the x-axis when x=3 is _______. Complete the table, and sketch a graph of f. x f(x) (x,y) 2 1 0 1 2