Comparing Functions - Pre Algebra

1. Plan A costs 20 dollars plus 5 dollars per hour. Plan B costs 8 dollars per hour. Which costs less for 3 hours?

   Plan B: 24 dollars, compared with 35 dollars for Plan A.

2. How is a function's rate of change found from a table to compare it with another function?

   Divide the change in output by the change in input between two rows; the larger quotient is the greater rate.

3. Which function is decreasing: $f(x) = -3x + 2$ or $g(x) = 2x - 1$?

   $f$, because its slope $-3$ is negative.

4. Which line is steeper: $y = -4x$ or $y = 2x$?

   $y = -4x$. Steepness depends on the absolute value of the slope, and $4 > 2$.

5. Function $f$ has slope 2 and $y$-intercept 3. How does its graph compare with $g(x) = 2x + 1$?

   The lines are parallel: same rate of change, with $f$ 2 units above $g$.

6. Car A travels $d = 55t$ miles. Car B goes 120 miles in 2 hours and 240 miles in 4 hours. Which car is faster?

   Car B, at 60 miles per hour compared with 55.

7. When $x$ increases by 1, how much more does $y = 6x$ increase than $y = 2x$?

   4 more. $y = 6x$ rises 6 per unit and $y = 2x$ rises 2 per unit.

8. Function A is $y = 2x + 7$. Function B has the points $(0, 1)$, $(1, 4)$, $(2, 7)$. Which has the greater rate of change?

   Function B. Its outputs rise 3 per unit of $x$, compared with 2 for A.

9. Which function has the greater rate of change: $f(x) = 3x + 1$ or $g(x) = 5x - 2$?

   $g$, because its slope 5 is greater than 3.

10. Which gives the larger output at $x = 5$: $f(x) = 3x$ or $g(x) = x + 12$?

    $g$. $g(5) = 17$, while $f(5) = 15$.

11. Which has the greater initial value: $y = 4x + 10$, or a function with the points $(0, 6)$ and $(1, 9)$?

    $y = 4x + 10$. Its value at $x = 0$ is 10, compared with 6.

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