Question
A 2-column table with 6 rows. The first column is labeled t with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 12, m, 4, 0, negative 4, negative 2.
If the table of the function contains exactly two potential turning points, one with an input value of –1, which statement best describes all possible values of m?
m ≥ –12
–12 < m < 4
m ≤ 4
m ≥ 4 or m ≤ –12
If the table of the function contains exactly two potential turning points, one with an input value of –1, which statement best describes all possible values of m?
m ≥ –12
–12 < m < 4
m ≤ 4
m ≥ 4 or m ≤ –12
Answers
Answer
1. A 2-column table with 7 rows. The first column is labeled x with entries negative 5, negative 3, negative 1, 1, 3, 5, 7. The second column is labeled f of x with entries 8, 4, 0, negative 2, negative 2, 0, 4.
Which is a valid prediction about the continuous function f(x)?
f(x) ≥ 0 over the interval [5, ∞).
f(x) ≤ 0 over the interval [–1, ∞).
f(x) > 0 over the interval (–∞, 1).
f(x) < 0 over the interval (–∞. –1).
2. A 2-column table with 6 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries 20, 0, negative 6, negative 4, 0, 0.
Which is an x-intercept of the continuous function in the table?
(–1, 0)
(0, –6)
(–6, 0)
(0, –1)
3. A 2-column table with 8 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3, 4. The second column is labeled f of x with entries negative 2, 0, 2, 2, 0, negative 8, negative 10, negative 20.
Which could be the entire interval over which the function, f(x), is positive?
(–∞, 1)
(–2, 1)
(–∞, 0)
(1, 4)
4. Which table shows a function that is increasing only over the interval (–2, 1), and nowhere else?
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 6, negative 3, negative 1, 1, 3, 6.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 2, negative 4, negative 1, 1, 4, 3.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 3, negative 5, negative 7, negative 6, 1, negative 1.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 5, 7, 1, 0, negative 4, negative 2.
5. A 2-column table with 6 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries negative 10, negative 8, negative 6, negative 4, negative 2, 0.
Which is an x-intercept of the continuous function in the table?
(0, –6)
(3, 0)
(–6, 0)
(0, 3)
6. A 2-column table with 6 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries negative 8, 0, 0, negative 2, 0, 12.
Which lists all of the y-intercepts of the continuous function in the table?
(0, 0)
(–1, 0), (2, 0)
(–1, 0), (0, 0)
(–1, 0), (0, 0), (2, 0)
7. A 2-column table with 8 rows. The first column is labeled x with entries negative 6, negative 5, negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 34, 3, negative 10, negative 11, negative 6, negative 1, negative 2, negative 15.
Using only the values given in the table for the function, f(x), what is the interval of x-values over which the function is increasing?
(–6, –3)
(–3, –1)
(–3, 0)
(–6, –5)
8. A local maximum of the function f(x) occurs for which x-value?
A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 16, negative 2, 0, 6, 0, negative 2.
–4
–3
–2
–1
9. A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries negative 10, 0, 0, negative 4, negative 6, 0.
Which is a y-intercept of the continuous function in the table?
(0, –6)
(–2, 0)
(–6, 0)
(0, –2)
10. A 2-column table with 7 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 6, negative 4, negative 1, negative 2, negative 5, negative 8, negative 16.
Which is a possible turning point for the continuous function f(x)?
(–3, –4)
(–2, –1)
(0, –5)
(1, –8)
Which is a valid prediction about the continuous function f(x)?
f(x) ≥ 0 over the interval [5, ∞).
f(x) ≤ 0 over the interval [–1, ∞).
f(x) > 0 over the interval (–∞, 1).
f(x) < 0 over the interval (–∞. –1).
2. A 2-column table with 6 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries 20, 0, negative 6, negative 4, 0, 0.
Which is an x-intercept of the continuous function in the table?
(–1, 0)
(0, –6)
(–6, 0)
(0, –1)
3. A 2-column table with 8 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3, 4. The second column is labeled f of x with entries negative 2, 0, 2, 2, 0, negative 8, negative 10, negative 20.
Which could be the entire interval over which the function, f(x), is positive?
(–∞, 1)
(–2, 1)
(–∞, 0)
(1, 4)
4. Which table shows a function that is increasing only over the interval (–2, 1), and nowhere else?
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 6, negative 3, negative 1, 1, 3, 6.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 2, negative 4, negative 1, 1, 4, 3.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 3, negative 5, negative 7, negative 6, 1, negative 1.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 5, 7, 1, 0, negative 4, negative 2.
5. A 2-column table with 6 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries negative 10, negative 8, negative 6, negative 4, negative 2, 0.
Which is an x-intercept of the continuous function in the table?
(0, –6)
(3, 0)
(–6, 0)
(0, 3)
6. A 2-column table with 6 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries negative 8, 0, 0, negative 2, 0, 12.
Which lists all of the y-intercepts of the continuous function in the table?
(0, 0)
(–1, 0), (2, 0)
(–1, 0), (0, 0)
(–1, 0), (0, 0), (2, 0)
7. A 2-column table with 8 rows. The first column is labeled x with entries negative 6, negative 5, negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 34, 3, negative 10, negative 11, negative 6, negative 1, negative 2, negative 15.
Using only the values given in the table for the function, f(x), what is the interval of x-values over which the function is increasing?
(–6, –3)
(–3, –1)
(–3, 0)
(–6, –5)
8. A local maximum of the function f(x) occurs for which x-value?
A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 16, negative 2, 0, 6, 0, negative 2.
–4
–3
–2
–1
9. A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries negative 10, 0, 0, negative 4, negative 6, 0.
Which is a y-intercept of the continuous function in the table?
(0, –6)
(–2, 0)
(–6, 0)
(0, –2)
10. A 2-column table with 7 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 6, negative 4, negative 1, negative 2, negative 5, negative 8, negative 16.
Which is a possible turning point for the continuous function f(x)?
(–3, –4)
(–2, –1)
(0, –5)
(1, –8)
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