Concept explainers
(a)
To calculate: The domain of the function
(a)
Answer to Problem 1PRE
Solution:
The domain of the function is
Explanation of Solution
Given:
The function,
Calculation:
The domain is the all possible input for any provided function.
Here, the domain will be
(b)
The range of the function
(b)
Answer to Problem 1PRE
Solution: The range is
Explanation of Solution
Given:
The range is all the possible outputs of a given function,
Here, for
Hence, the range is
(c)
The x-intercept(s) of the function
(c)
Answer to Problem 1PRE
Solution: There is no x-intercept.
Explanation of Solution
Given:
To find the x-intercept(s), solve the equation
This is false,
Hence, there is no x-intercept.
(d)
The y-intercept(s) of the function
(d)
Answer to Problem 1PRE
Solution: The y-intercept is
Explanation of Solution
Given:
To find the y-intercept(s), evaluate
The y-intercept is 3.
(e)
The asymptotes if applicable for the function
(e)
Answer to Problem 1PRE
Solution: No asymptotes.
Explanation of Solution
Given:
Since the given function is a constant function, i.e., no curve involved.
Hence, no asymptotes.
(f)
The intervals over which the function
(f)
Answer to Problem 1PRE
Solution: Never increasing.
Explanation of Solution
Given:
Since the given function is a constant function, i.e., no curve involved.
Hence, never increasing.
(g)
The intervals over which the function
(g)
Answer to Problem 1PRE
Solution: Never decreasing.
Explanation of Solution
Given:
A function is an increasing function if the function values increase within the given interval. Similarly, a function is a decreasing function if the function values decrease within the given interval.
Since the given function is a constant function, i.e., no curve involved.
Hence, the given function
(h)
The match of the function
(h)
Answer to Problem 1PRE
Solution: Graph E.
Explanation of Solution
Given:
Since the given function is a constant function where for any value of x the output is 3,
Hence the graph will be a horizontal straight line crossing the y-axis at
The correct match will be graph E
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Chapter 4 Solutions
College Algebra Essentials
- In Exercises 45–46, the domain of each piecewise function is (-*,). a. Graph each function. b. Use the graph to determine the function's range. S 5 if xs -1 45. f(x) = -3 if x> -1 | 2x if x <0 46. f(x) = if x2 0arrow_forwardMA.912.F.1.5 Date: Period: Callie and her friend Elena are reading through different novels they checked out from their school library last Tuesday. Callie's progress through her novel can be modeled by the function p(d) = -25d +318, where p(d) represents the number of pages remaining to be read and d is the number of days since receiving the book. Elena's progress through her novel is modeled by the graph below. АУ # Pages Left 400 350 300 250 200 * 150 100 50 (3275) (8,75) 2 3 4 5 6 7 # Days Part A. Which student's novel has more pages to read? 8 9 10 11 Part B. Assuming they both continue to read at a constant rate, which student will complete their novel first?arrow_forwardII. Find the domain and range and sketch the graph of the functionarrow_forward
- Write the function whose graph is the graph of y=x², but is shifted down 1 unit.arrow_forward3. Determine the domain and range of the function y = 2c0sxarrow_forward2. Let g(x) =-2(x – 2)² + 8 Determine the equation of the axis of symmetry. a. b. Determine the domain of the function. C. Determine the range of the function. d. Determine the y-intercept, if there is any. Write your answer as an ordered pair. Determinę the x-intercept(s), if there is any. Write your answers as ordered pairs. e.arrow_forward
- 1. Use the graph to the right for a - d. What is the name of the parent function? а. b. Identify the domain: C. Identify the range: d. End Behavior: As x - f(x)- and As x f(x) -arrow_forwardThe function graphed is of the formy=asinbx or y=acosbx, where b > 0. Determine the equation of the graph.arrow_forwardQ4. Let y = a? - 6x +5 be given. (a) Find x and y intecepts (if any) of the given function. b) Find the vertex. Sketch the graph of the given function in question 4.arrow_forward
- The domain of the piecewise function is (−∞,∞). a. Graph the function. b. Use your graph to determine the function's range.arrow_forwardWhich of the functions has the y-axis as the line of symmetry?arrow_forward2. Sketch graph of each function, including the basic function and all intermediate curves. y=-2x+3 y=(-x+2)-3 a. b.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage