Free Case Study On Answers To Exercises

1. Yes, it passes the test. A vertical line does not intersect the function in more than one place.
2. This is a piecewise function and the range is y ≥ 0.
3. The domain is x ≥ -5. The function is not defined for x < -5. 4. The only x intercept occurs at point (3,0) 5. The y intercept occurs at point (0,3) 6. It is a piecewise function. Each piece is linear. 7. The value is f(x=2) = 3. 8. Yes, the binomial function passes the vertical line test. A vertical line does not intersect the function in more than one place.
9. The range is y ≥ 2.
10. The domain is all values x can take on, namely, all real numbers.
11. There is no x intercept. The lowest value of the function is f(x=-3) = 2. Therefore f(x) never reaches zero so it does not cross the x axis.
12. The y intercept occurs at point (0,3)
13. Yes, the cubic function passes the test. A vertical line does not intersect the function in more than one place.
14. The figure shows that the function covers all y values. Therefore, the range is all real numbers.
15. The domain is all real numbers. The x coordinate can take on any value.
16. There is only one x intercept and it occurs at point (1,0)
17. The y intercept occurs at point (0,1)
18. The cubic function evaluated at x=2 is f(2) = -1.
19. The inverse function is g(y) = 3y-5
20. The inverse function is g(y) = 6y-7
21. The new function is f+gx = 4x+3
22. The new function is f-gx = 2x-1.
When it is evaluated at x=5, the result is f-g5 = 9
23. The new function is:
fg(x)=3x+1x+2=3x2+6x+x+2=3x2+7x+2
24. The new function is:
fgx=3x+1x+2
When it is evaluated at x=1, the result is,
fg1=43