Purchase Solution

Functions and their graphs

Not what you're looking for?

Ask Custom Question

1. f(x)= 2x+5 if -3 <= X <0
-3 if x=0
-5x if x>0

a. Find the domain of each function.
b. Locate any intercepts.
c. Graph each function
d.Based on the graph find the range.
e. Is f continuous on its domain?

2. If f(x)= int(x/2) Find, (a) f(1.2) (b) f(1.6) (c) f(-1.8)

3. Graph y= [x], then on the same screen graph y=2[x],followed by y=4[x],followed by Y=1/2[x]. what pattern do you observe?Can you predict the graph of Y=1/4[x]? Of Y=5[x]?

[x] = Absolute X.

4. Find the function that is finally graphed after the following transformation are applied to the graph of Y= square root of X.
(a) Reflect about x-axis
(b) shift right 3 units.
(c) Shift Down 2 units.

5. If (3,6) is a point on the graoh of Y=f(x) which of the following point must be on the graph of Y=f(-x).
(a) (6,3)
(b) (6,-3)
(c) (3,6)
(d) (-3,6)

6. Suppose that the function Y=f(x) is decreasing on the interval (-2,7).
(a) Over what interval is the graph of Y=f(x+2) decreasing.
(b) Over what interval is the graph of Y=f(x-5) decreasing.
(c) What can be said about the graph of Y= -f(x).
(d) What can be said about the graph of Y= f(-x).

7. Graph each function using the technique of shifting,compressing,stretching and or reflecting. Start with graph of the basic function ( for example Y=x^2) and show all the stages. Be sure to show atleast 3 key points. Find the domain and range of each function.

f(x)= 3(x-2)^2 + 1.

8. f(x)= -3x^2 + 5x
(a). Is the point (-1,2) on the graph of f.
(b) If x= -2, what is f(x)? What the point is on the graph of f.
(c) If f(x)= -2, What is x? What point are on the graph of f.
(d) what is the domain of f.
(e) List the x intercepts in any of the graph of f.
(f) List the y intercept, if there is one, of the graph of f.

Purchase this Solution
Solution Summary

Functions and their graphs are exemplified.

Solution Preview

Functions and their Graphs
1. f(x)= 2x+5 if -3 <= x <0
-3 if x=0
-5x if x>0

a. Find the domain of each function.
b. Locate any intercepts.
c. Graph each function
d.Based on the graph find the range.
e. Is f continuous on its domain?

a) We can observe from the definition that the function is defined for all x more than or equal to -3. Hence the domain is
b) Given that f(x)=-3 when x=0. So, y-intercept is (0, -3). Further if 2x+5=0, we get x=-5/2. Hence the x intercept is (-5/2, 0)
c)
d) the curve goes down without limit and does not cross 5. Hence the range of the function is
e) from the graph it is clear that the function is not continuous at x=0.

2. If f(x)= int(x/2) Find, (a) f(1.2) (b) f(1.6) (c) f(-1.8)
a) f(1.2)=int(0.6)=0
b) f(1.6)=int(0.8)=0
c)f(-1.8)=int(-0.9)=-1

3. Graph y= [x], then on the same screen ...

Purchase this Solution
Free BrainMass Quizzes
Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Probability Quiz

Some questions on probability

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

View More Free Quizzes
Related BrainMass Solutions

  • Examples of Functions : Exponentials, Graphs and Usefulness

    Discuss these functions and their graphs with your classmates. 2. Given the values 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, x, and y, form each of the following: ? A linear equation in one variable ? A linear equation in two variables ?

  • Functions and Their Graphs

    Equations of functions given by their graphs are expressed.

  • Finding Trigonometric Functions with a Graphs

    29185 Trigonometry - Match Functions With Graphs Match the attached functions with their graphs. Thank you.. Match the function with its graph. Which is the correct answer?

  • Function/algebra

    2 c.y = 3 d.y = 0 6.Exponential Functions and Their Graphs Evaluate 4square root 6^ to six significant digits.

  • Cos x and Sin(x + 90)

    When we draw the graphs of the functions g(x) = cos x and f(x) = sin x by taking a few points in their domain and taking at least 2 complete cycles for both for a better picture, we observe that the graphs are essentially the same, except that the graph

  • Graphical representation of functions

    Discuss these functions and their graphs with your classmates. 2. Given the values 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, x, and y, form each of the following: ? A linear equation in one variable ? A linear equation in two variables ?

  • Functions and Graphs : Heart Disease, Cancer and AIDS - Trends and Real World Implications

    Functions and Graphs are discussed with regard to Heart Disease, Cancer and AIDS. Trends and Real World Implications are investigated. The solution is detailed and well presented.

  • Graphing Functions Differentiation

    47921 Graphing Functions Differentiation Differentiation of graphs for Celcius and Farenheit functions see attachment pls Differentiation of graphs for Celcius and Farenheit functions Solution.

  • Exponential Functions and their Inverse and Graphs

    152595 Questions are about exponential functions, inverse of a functions, graphing of exponential functions, and investigation of their graphs as the argument changes. Please provide graphs. 1. One example of an exponential function is f(x) = 4x.

  • Quadratic Equations, Graphs, Rational Inequalities and Word Problems

    Includes the following Exercises: -Quadratic Functions and Their Graphs -Quadratic and Rational Inequalities; Equations, Functions and Inequalities -Quadratic Equations, Functions, and Inequalities Maximum height.

View More Related Solutions