Question

which statement below is true regarding the functions pictured? both functions have a multiplying pattern; both functions are linear; both functions have a y-intercept of 3; both functions are increasing

Explanation:

Step1: Analyze Table Function

The table has x-values: 0,1,2,3,4,5 and y-values: 3,5,7,9,11,13. Calculate the rate of change: $\frac{5-3}{1-0}=2$, $\frac{7-5}{2-1}=2$. This is a constant rate, so it's linear, with equation $y=2x+3$. It is increasing, has a y-intercept of 3, and an additive pattern.

Step2: Analyze Graph Function

The graph is a straight line (linear). It rises from left to right, so it is increasing. To check y-intercept: when $x=0$, the line crosses at $y=3$. The rate of change is positive (additive, not multiplying).

Step3: Evaluate Each Option

- "Both functions have a MULTIPLYING pattern": False, both have additive (constant slope) patterns.
- "Both functions are linear": True, but let's check others.
- "Both functions have a y-intercept of 3": True, but check the last option.
- "Both functions are increasing": True? Wait, re-verify: table y increases as x increases, graph rises. But wait, let's confirm all:
Wait, linear functions with positive slope are increasing. But let's check which is all true. Wait, the table is $y=2x+3$, graph is a line with positive slope, y-intercept 3. Now, check each option:
1. Multiplying pattern: No, it's additive (each x increases by 1, y increases by 2). So false.
2. Both are linear: Yes, table is linear (constant rate), graph is straight line (linear).
3. Both have y-intercept 3: Table has y=3 when x=0, graph crosses y-axis at 3: yes.
4. Both are increasing: Table y goes up as x goes up, graph rises: yes. Wait, but let's check again. Wait, maybe I misread the graph? No, the graph is a rising line. But wait, let's check which statements are true. Wait, but let's check if all are true? No, wait the first option is false. Now, let's confirm:

Wait, the table: x=0,y=3; x=1,y=5: difference +2. So linear, increasing, y-intercept 3. Graph: straight line, starts at (0,3), goes up: linear, increasing, y-intercept 3.

Wait, but the options: let's check each:
- "Both functions have a MULTIPLYING pattern": False, it's additive.
- "Both functions are linear": True
- "Both functions have a y-intercept of 3": True
- "Both functions are increasing": True

Wait, but maybe the graph is not starting at 3? Wait no, the table has x=0,y=3, which is y-intercept. The graph's line passes through (0,3) as per the grid. Wait, but maybe the question has only one true answer? Wait, no, let's recheck. Wait, maybe I made a mistake. Wait, the table: when x=0, y=3; x=1,y=5: slope 2, so $y=2x+3$. The graph: let's see, the grid: the line goes from (0,3) to (2,7), which is slope $\frac{7-3}{2-0}=2$, so same as table? No, but regardless, it's linear, increasing, y-intercept 3.

Wait, but the options: maybe all except first are true? But no, let's check the question again. Wait, maybe the graph is not linear? No, it's a straight line. Wait, maybe the "multiplying pattern" is exponential? No, this is linear, so additive.

Wait, but let's check each option again:
1. Multiplying pattern: False, because y increases by a constant addend, not a multiplier.
2. Both are linear: True, table has constant rate of change, graph is straight line.
3. Both have y-intercept 3: True, table has y=3 at x=0, graph crosses y-axis at 3.
4. Both are increasing: True, as x increases, y increases for both.

Wait, but maybe the question has multiple correct? But let's check the original problem. Wait, maybe I misread the table. The table: x values 0,1,2,3,4,5; y values 3,5,7,9,11,13. Yes, that's correct. The graph is a straight line going up, starting at (0,3).

Wait, but let's confirm which are true. All options except the first are true? But that can't be. Wait, maybe the graph's y-intercept is not 3? Let's look at the grid: the bottom left is (0,0), the line crosses the y-axis at the 3rd grid line, so y=3. Correct.

Wait, but maybe the question considers that "linear" is true, "y-intercept 3" is true, "increasing" is true. But maybe the problem has multiple correct? But let's check again. Wait, no, maybe I made a mistake with "multiplying pattern": multiplying pattern would be exponential, like y=3*2^x, but here y increases by 2 each time, so additive. So that's false.

Wait, but the question says "which statement below is TRUE". Maybe multiple are true? But let's list all true ones.

Wait, no, let's re-express:

For the table function:
- Linear: Yes (constant slope)
- y-intercept 3: Yes (x=0,y=3)
- Increasing: Yes (y increases as x increases)
- Multiplying pattern: No (additive)

For the graph function:
- Linear: Yes (straight line)
- y-intercept 3: Yes (crosses y-axis at 3)
- Increasing: Yes (rises left to right)
- Multiplying pattern: No

So the true statements are:
- Both functions are linear
- Both functions have a y-intercept of 3
- Both functions are increasing

But wait, maybe the graph is not linear? No, it's a straight line. Wait, maybe the table is not linear? No, constant rate of change.

Wait, but maybe the question has all these as correct? But let's check again.

Wait, maybe I misread the y-values. The table y-values: 3,5,7,9,11,13. Yes, each +2. So linear.

Answer:

B. Both functions are linear
C. Both functions have a y-intercept of 3
D. Both functions are increasing