Through which points does the function below pass?
y=2(x+2)−1
To determine through which points the function y=2(x+2)−1 passes, let's proceed methodically.
Step 1: Simplify the expression of the linear function:
The given function is y=2(x+2)−1. Distribute the 2 over the terms inside the parenthesis:
y=2x+4−1
Simplify further by combining like terms:
y=2x+3
Step 2: Evaluate the function at different x-values to find which points lie on the line represented by the function y=2x+3.
Step 3: Check each of the provided choice points:
- For choice (0,0): Substituting x=0 into y=2x+3, we get y=2(0)+3=3. This does not match y=0.
- For choice (10,13): Substituting x=10 into y=2x+3, we get y=2(10)+3=23. This does not match y=13.
- For choice (5,13): Substituting x=5 into y=2x+3, we get y=2(5)+3=13. This matches y=13, so this point lies on the line.
- For choice (4,13): Substituting x=4 into y=2x+3, we get y=2(4)+3=11. This does not match y=13.
Therefore, the point through which the given function passes is (5,13).