Sample Work Assignment
Algebra 1A
Chapter 4
You must show all work. No decimal answers.
Sketch a graph to represent the situation. Label each section.
1. The temperature changed as Nadia preheated the oven, baked the cookies, and turned the oven off.
For the table, determine whether the relationship is a function. Then represent the relationship using words, an equation, and a graph.
2.
x y
0 4
1 3
2 2
3 1
Write a function rule that represents each sentence.
3. 11 less than the product of a number y and -2 is z.
4. 5 less than the quotient of a number n and 4 is m.
Find the range of each function for the given domain.
5. f(x) = -2x + 1; {-6, -2, 0}
6. f(x) = x3 + 1; {-2, -1, 3}
Tell whether the sequence is arithmetic or not. If the sequence is arithmetic, write a function rule to represent it.
7. -19, -11, -3, 5, . . . . . .
8. Write a function rule for the area of a rectangle whose length is 5 in. more than its width. What is the area of the rectangle when its width is 8 in.?
1. To sketch a graph representing the temperature changing as Nadia preheated the oven, baked the cookies, and turned the oven off, you will need to label each section of the graph based on the different stages. For example:
- Label the first section as "Preheating" and show the temperature increasing gradually.
- Label the second section as "Baking" and show a relatively constant temperature.
- Label the third section as "Turning off" and show the temperature decreasing gradually.
2. To determine whether the relationship given in the table is a function, you need to check if each input (x value) is paired with one and only one output (y value). In this case, the relationship is a function because each x value is paired with a unique y value.
To represent the relationship using words, you can say that "y is equal to 4 minus x" or "y equals four minus x."
The equation representing the relationship is y = 4 - x.
To graph this relationship, plot the points (0, 4), (1, 3), (2, 2), and (3, 1) on a coordinate plane and connect them with a straight line.
3. The sentence "11 less than the product of a number y and -2 is z" can be written as an equation: -2y - 11 = z. This equation represents the relationship between y and z.
4. The sentence "5 less than the quotient of a number n and 4 is m" can be written as an equation: n/4 - 5 = m. This equation represents the relationship between n and m.
5. To find the range of the function f(x) = -2x + 1 for the given domain {-6, -2, 0}, substitute each value from the domain into the function and calculate the corresponding range values:
- For x = -6: f(-6) = -2*(-6) + 1 = 13.
- For x = -2: f(-2) = -2*(-2) + 1 = 5.
- For x = 0: f(0) = -2*0 + 1 = 1.
Therefore, the range of the function for the given domain is {13, 5, 1}.
6. To determine whether the sequence -19, -11, -3, 5, ... is arithmetic, you need to check if there is a common difference between consecutive terms. In this case, the common difference is 8, so the sequence is arithmetic.
To write a function rule representing this arithmetic sequence, you can use the formula: an = a1 + (n - 1)d, where an represents the term at position n, a1 is the first term, and d is the common difference. In this case, the function rule is: f(n) = -19 + (n - 1)8.
7. The function rule for the area of a rectangle whose length is 5 in. more than its width can be represented as follows: A(w) = (w + 5)w, where w represents the width.
To find the area of the rectangle when its width is 8 in., substitute w = 8 into the function rule: A(8) = (8 + 5) * 8 = 104 square inches. Therefore, the area of the rectangle with a width of 8 inches is 104 square inches.
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8. L = W + 5 = 8 +5 = 13
Area = L * W = ?