1. The problem is to analyze the four tables of (x, y) pairs and determine the nature of the relationships they represent. 2. We will check if each table represents a function, and if so, what type of function it might be (constant, linear, etc.). 3. Table Q: Points (-2, -3), (1, 3), (3, -3), (5, 3). - The y-values alternate between -3 and 3, not consistent with a function since for x=3 and x=5, y changes. 4. Table R: Points (-1, -5), (2, 4), (3, 7), (4, 10). - Check if linear: Calculate slope between points. - Slope between (-1, -5) and (2, 4): $$m=\frac{4 - (-5)}{2 - (-1)}=\frac{9}{3}=3$$ - Slope between (2, 4) and (3, 7): $$m=\frac{7 - 4}{3 - 2}=3$$ - Slope between (3, 7) and (4, 10): $$m=\frac{10 - 7}{4 - 3}=3$$ - Constant slope 3, so linear function. - Equation form: $$y=mx+b$$ - Use point (-1, -5): $$-5=3(-1)+b \Rightarrow b=-5+3=-2$$ - Final equation: $$y=3x - 2$$ 5. Table S: Points (-2, 3), (1, 3), (3, 3), (5, 3). - All y-values are 3, so this is a constant function. - Equation: $$y=3$$ 6. Table T: Points (3, 4), (4, 5), (3, -4), (4, -5). - For x=3, y=4 and y=-4; for x=4, y=5 and y=-5. - Not a function since x-values repeat with different y-values. Final answers: - Q and T are not functions. - R is linear with equation $$y=3x - 2$$. - S is constant with equation $$y=3$$.