More STAAR problems.
Administered May 2019
Read each question carefully. For a multiple-choice question, determine the
best answer to the question from the four answer choices provided. For a
griddable question, determine the best answer to the question.
31. The table represents some points on the graph of an exponential function.
Which function represents the same relationship?
A f(x) = 15(5/6)x
B f(x) = 18(6/5)x
C f(x) = 15(6/5)x
D f(x) = 18(5/6)x
Answer: B f(x) = 18(6/5)x
Two observations.
First, the numbers are getting bigger, which means growth, not decay. So the base has to be greater than one (6/5) not less than one (5/6). Eliminate choices A and D.
Second, when x = 0, (6/5)0 = 1. We are left with just the initial amount. Since f(x) = 18, the initial amount in the function must be 18, which is choice B.
Other observations: 15 was just silly. And you could graph them and check the table of values, if you really needed to.
32. The table shows the amount of pet food in cups remaining in an automatic feeder as a
function of the number of meals the feeder has dispensed.
Based on the table, which function models this situation?
F f(n) = -3n + 24
G f(n) = -1/3 n + 16
H f(n) = -3n + 64
J f(n) = -1/3 n + 8
Answer: F f(n) = -3n + 24
Find the slope:
(15 - 21) / (3 - 1) = -6 / 2 = -3
Eliminate choices G and J
If the slope is -3 and you have a point of (1, 21), then you can easily see that (0, 24) is also a point on the graph. This gives you choice F.
If you didn't see that, write the following equation:
y - 21 = -3x + 3
y = -3x + 24
33. The graph of f(x) = x2 was transformed to create the graph of g(x) = f(x) - 9. Which
statement about the graphs is true?
A The graph of g is a reflection of the graph of f across the x-axis.
B The vertex of the graph of g is 9 units to the right of the vertex of the graph of f.
C The graph of g is a reflection of the graph of f across the y-axis.
D The y-intercept of the graph of g is 9 units below the y-intercept of the graph of f.
Answer: D The y-intercept of the graph of g is 9 units below the y-intercept of the graph of f.
The output of f(x) is the y-coordinate on the graph.
If g(x) subtracts 9 units from f(x), then the y-coordinate will be 9 units lower.
That is, the graph shifts down.
There is no reason why the graph should be a reflection across either axis. To make the graph shift to the right, the -9 would have to be inside the parentheses, where it would affect the input and not the output.
34. The expression (x22)(x7)3 is equivalent to xp. What is the value of p?
Record your answer and fill in the bubbles on your answer document.
Answer: 43
The rules for exponents say you have to multiply the 7 and 3 and then add 22 to the result.
22 + 7 * 3 = 43
If you're aren't sure why that is, consider writing out the second term three times.
(x22)(x7)(x7)(x7)
The sum of the exponents is 22 + 7 + 7 + 7 = 43.
35. The graph of linear function k passes through the points (-7, 0) and (1, 8)
Which statement must be true?
A The slope of the graph is -4/3
B The graph of k passes through the point (-1, -8)
C The zero of k is 7.
D The x-intercept of the graph of k is -7.
Answer: D The x-intercept of the graph of k is -7.
The blank graph is given as an aid. You can plot the two points, figure out the slope from the rise and run and then check which of the answers is true.
However, if you read all the choices, that wouldn't be necessary.
Keep in mind that "the zero of k" and "the x-intercept" mean the same thing. Where does the line cross the x-axis. At the x-axis, the value of y is 0.
But we are given the point (-7, 0), so we know that the x-intercept (the zero) is -7. That is choice D.
It is easy to tell from the points that the slope is rising, and therefore positive, so -4/3 is not correct for the slope. (It is, in fact, 1 if you want to check.)
Likewise, if the y values are rising between 0 and 8 then a value of -8 is inconsistent.
Choice C is out because we know it is -7, not +7.
More to come. Comments and questions welcome.
More STAAR problems.
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