NJGPA Interpreting Functions and Key Features from Graphs and Tables (Algebra I) 4

Question 1

A graph shows f(x) = 0 at x = 2 and x = -5. Which factored form could represent this function?

Accepted Answer

(x - 2)(x + 5)

Answer

Zeros at x = 2 and x = -5 correspond to factors (x - 2) and (x + 5).

Question 2

A table of values for f(x) shows: x = -2 gives f = 4, x = 0 gives f = 0, x = 2 gives f = 4. What symmetry does this suggest?

Accepted Answer

The function is symmetric about x = 0 (the y-axis)

Answer

Equal outputs at x = -2 and x = 2 (same distance from 0) indicate symmetry about the y-axis.

Question 3

On a graph, the interval where f(x) is increasing transitions to decreasing at x = 3. What occurs at x = 3?

Accepted Answer

A maximum value

Answer

The transition from increasing to decreasing marks a local maximum at x = 3.

Question 4

A table shows inputs doubling: x = 1, 2, 4, 8 with outputs 0, 3, 6, 9. What type of function might this be?

Accepted Answer

Logarithmic

Answer

When inputs grow exponentially but outputs grow linearly (by equal amounts), the function is logarithmic.

Question 5

A graph of a function has a y-intercept at (0, 6) and passes through (3, 0). What is its slope?

Accepted Answer

-2

Answer

Slope = (0 - 6)/(3 - 0) = -6/3 = -2.

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