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;...

(Parte 2 de 2)

Domain=

Domain=

12. For and g(x) =x+8

a. =

b. =

c. =

d.

13. For and g(x) =2x+3

a. =

b. =

c.

d. =

14. For and

a. =

b.

c.

d.

15. For and

a. =

b.

c. =

d.

16. For and

a. =

b. =

c.

d. =

17. For and

a. =

b. =

c.

d.

18. For and

a.

b. =

c.

d.

19. For and

a. =

b. =

c. =

d. =

20. For and

a.

b. =

c. =

d.

Section 2.7. Inverse Functions

1. Find f​(g​(x)) and g​(f​(x)) and determine whether the pair of functions f and g are inverses of each other.

and

2. Find f​(g​(x)) and g​(f​(x)) and determine whether the pair of functions f and g are inverses of each other.

and

3. The function is ​one-to-one. Find an equation for, the inverse function.

4. Find a formula for the inverse.

5. The function is​ one-to-one. Find an equation for, the inverse function.

6. The function is​ one-to-one. Find an equation for, the inverse function.

7. The function is​ one-to-one. Find an equation for, the inverse function.

8. The function ​, x ≠ ​0, is​ one-to-one. Find an equation for ​, the inverse function.

9. Given the function ​

​(a) Find .

​(b) Graph f and in the same rectangular coordinate system.

​(c) Use interval notation to give the domain and the range of f and .

10. Given the function ,

​(a) Find .

​(b) Graph f and in the same rectangular coordinate system.

​(c) Use interval notation to give the domain and the range of f and

11. Given the function ,

​(a) Find .

​(b) Graph f and in the same rectangular coordinate system.

(c) Use interval notation to give the domain and the range of f and

12. Given the function

​(a) Find .

​(b) Graph f and in the same rectangular coordinate system.

(c) Use interval notation to give the domain and the range of f and

13. Given the function

​(a) Find .

​(b) Graph f and in the same rectangular coordinate system.

(c) Use interval notation to give the domain and the range of f and

14. Given the function

​(Hint: To solve for a variable involving an nth​ root, raise both sides of the equation to the nth​ power, .

​(a) Find

​(b) Graph f and in the same rectangular coordinate system.

​(c) Use interval notation to give the domain and the range of f and

Section 2.8. Distance and Midpoint Formulas; Circles

1. Find the distance between the pair of points.

​(9, 3) and (21, 8)

2. Find the distance between the pair of points ​(2​,1​) and ​(9​,8​). If ​necessary, express the answer in simplified radical form and then round to two decimal places.

3. Find the distance between the pair of points.

​(0, 0) and (4, 3)

4. Find the midpoint of the line segment with the given endpoints.

​(2, 8) and (6, 4)

5. Find the midpoint of the line segment whose endpoints are given.

​(−4, 6), (−2, 7)

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

Center​(0, 0), r=4

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

Center (6, 8), r=10

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

Center (−8, −6), r=10

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

Center (6, 5), r =

10. Write the standard form of the equation of the circle with its center at (−1, 0), and a radius of

8.

11. 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.

12. 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.

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

14. Give the center and radius of the circle described by the equation and graph the equation. Use the graph to identify the domain and range.

15. 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.

16. Give the center and radius of the circle described by the equation and graph the equation. Use the graph to identify the domain and range.

Section 3.1. Quadratic Functions

1. 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.

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

3. 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.

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

Section 3.2. Polynomial Functions and Their Graphs

1. 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.

2. 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. Find the zeros for the given 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.

8. 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.

Section 3.3. Dividing Polynomials; Remainder and Factor Theorems

1. In the following​ problem, divide using long division. State the​ quotient, q(x), and the​ remainder, r(x).

2. Divide.

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

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

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

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

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

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

9. Divide using synthetic division.

10. Divide using synthetic division.

11. Divide using synthetic division.

12. Divide using synthetic division.

(Parte 2 de 2)

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