Transformations of Functions; Combinations of Functions; Composite Functions; Inverse Functions; Distance and Midpoint Formulas; Circles, Quadratic Functions; Polynomial Functions and Their Graphs; Dividing Polynomials; Remainder and Factor Theorems.

Transformations of Functions; Combinations of Functions; Composite Functions;...

Quiz for Exam 3

Section 2.5. Transformations of Functions

1. Use transformations of to graph the following function:

2. Begin by graphing the absolute value​ function, Then use transformations of this graph to graph the given function.

3. Use transformations of the graph of ​ to determine the graph of the given function.

4. First find . Then determine the domain for each function.

=

Domain=

(f

Domain=

Domain=

Domain=

5. First find . Then determine the domain for each function.

=

Domain=

(f

Domain=

Domain=

Domain=

6. For and g(x) =3x+5

a. =

b. =

c. =

d.

7. For and

a. =

b. =

c. =

d.

8. Given the function ​

​Find .

9. Given the function ​

​Find .

10. Find the distance between the pair of points ​(4​,1​) and ​(9​,6​). If​ necessary, express the answer in simplified radical form and then round to two decimal places.

11. Find the midpoint of the line segment whose endpoints are given (−10, −7), (2, −10).

12. Write the standard form of the equation of the circle with the given center and radius.

Center (−6, 8)​, r=10

13. Give the center and radius of the circle described by the equation and graph the equation. Use the graph to identify the​ relation's domain and range.

14. Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation of the​ parabola's axis of symmetry. Use the graph to determine the domain and range of the function.

15. Determine whether the function is a polynomial function. If it​ is, identify the degree.

A. It is a polynomial. The degree of the polynomial is: ___

B. It is not a polynomial.

16. Determine whether the function is a polynomial function. If it​ is, identify the degree.

A. It is a polynomial. The degree of the polynomial is ___

B. It is not a polynomial.

17. Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the​ x-axis or touches the​ x-axis and turns around at each zero.

18. Divide using long division. State the​ quotient, q(x), and the​ remainder, r(x).

19. Divide using synthetic division.

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