NJGPA Interpreting Functions and Key Features from Graphs and Tables (Algebra I) 2

Question 1

A table shows x-values 0, 1, 2, 3 and y-values 5, 8, 11, 14. What is the rate of change?

Accepted Answer

3

Answer

The y-value increases by 3 for each increase of 1 in x, so the rate of change is 3.

Question 2

On a graph of f(x), the function is above the x-axis for x < -2 and x > 4. Where is f(x) positive?

Accepted Answer

x < -2 and x > 4

Answer

A function is positive where its graph lies above the x-axis, which is x < -2 and x > 4.

Question 3

A function's graph shows a maximum value of 9 at x = 3. What does this vertex represent?

Accepted Answer

The highest output value the function reaches

Answer

The maximum value of 9 represents the highest output (y-value) the function achieves.

Question 4

A table for a linear function shows the points (2, 7) and (6, 15). What is the y-intercept?

Accepted Answer

3

Answer

The slope is (15-7)/(6-2) = 2, so using point (2,7): 7 = 2(2) + b gives b = 3.

Question 5

A graph shows a function that is decreasing on the interval (1, 5). Which statement is true?

Accepted Answer

f(1) > f(5)

Answer

A decreasing function has larger outputs at smaller inputs, so f(1) > f(5).

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