Algebra Question of the Day

1. Function $f$, because $f(3)=-1$ and $-1>0$.
2. Function $g$, because $g(3)=0$ and $0>-1$. (correct answer)
3. They are equal because both are decreasing.
4. Function $f$, because $f(3)=1$ and $1>0$.

Explanation: This question tests your ability to work with functions represented in different ways—like formulas, graphs, and tables—and compare their properties. Functions can be shown in multiple ways: an equation gives you a formula to calculate with, a graph shows the visual pattern, a table lists specific input-output pairs, and a verbal description explains the function in words. Each representation makes different features easy to see—graphs show maximums clearly, formulas make y-intercepts obvious (just set x = 0), and tables give you exact values to read directly. For function f given by f(x)=5-2x, at x=3, f(3)=-1; for function g in the table, g(3)=0, so compare -1 and 0 at that point. Choice B correctly identifies that function g has the greater output at x=3 because 0 > -1. If choice A was your pick, that's fine—recalculate f(3) to see it's negative. When comparing functions in different forms: (1) Identify what property you're comparing, (2) Extract that property from each representation using the appropriate method (substitute for formulas, read coordinates from graphs, find values in tables), (3) Compare the extracted values. Example: to compare y-intercepts, find where x = 0 in the formula, look where the graph crosses the y-axis, or find y when x = 0 in the table! Know what each representation shows best: formulas are great for calculating specific values and seeing patterns in the equation; graphs excel at showing maximums, minimums, and overall shape; tables are perfect for finding exact values at specific points; descriptions summarize key features. Use each representation's strengths!