Algebra 9.5 Worksheet Comparing Functions Answer Key

So, you’ve tackled the Algebra 9.5 Worksheet on comparing functions. And now you’re staring at that answer key, wondering if it’s friend or foe. I get it. We’ve all been there, clutching a half-crumpled worksheet like a treasure map that might lead to a D-.

First things first: breathe. This isn’t a test of your worth as a human being. It’s just a page full of lines, slopes, and the occasional table that looks like it was drawn by a caffeinated squirrel.

You’re comparing functions, right? Like, saying which one grows faster, which one starts higher, or which one just gives up and flattens out. That’s basically the Olympics of Algebra.

Why do we even do this?

Because the universe wants you to decide between a linear function (boring, predictable) and an exponential one (wild, takes off like a rocket). It’s like choosing between a reliable sedan and a sports car that might explode.

The answer key isn’t a villain. It’s more like that friend who tells you, “Hey, you forgot to carry the one… again.” Annoying? Yes. Helpful? Also yes.

Let’s talk about that one question with the graph.

You know the one. It shows two lines crossing, and you have to say which function has the greater rate of change. Spoiler: it’s usually the steeper line. If the line is so steep it looks like it’s trying to escape the page, that’s your winner.

But wait—sometimes the answer key says, “Neither, they’re equal at x=3.” And you’re like, “Cool, thanks for nothing, math.” That’s okay. Math loves drama.

Now, the tables. Oh, the tables. You get two lists of y-values, and you have to guess who’s going to win in the long run. Hint: if one column doubles every step, that crazy exponential function will destroy the other one by the time you hit x=10. It’s not even close.

The classic trick: y-intercept.

That’s where the function starts at x=0. If one starts at 50 and the other at 2, guess which one is ahead at the beginning? The 50 one. But don’t get cocky—the slow starter might roar past like a cheetah on espresso later.

Comparing Linear Functions Worksheet Answer Key | TAFT Independent

Here’s where the answer key can save your bacon. It tells you if you missed that the exponential function eventually wins. Because in real life, starting late is fine if you have a growth spurt. I’m looking at you, puberty and compound interest.

Rhetorical question time: have you ever compared two functions and felt like you were comparing apples and… angry porcupines?

Yes? Then you’re doing it right. One function might be linear (same difference every time), and the other might be quadratic (getting bigger, then smaller, then confusing). The answer key says, “Hey, check the graph—the quadratic bends. See that U-shape? That’s your clue.”

And for heaven’s sake, read the table headers. I once saw a kid swear the answer was “E” because they thought the columns were labeled “Number of Pizza Slices” and “Happiness Level.” No. It’s x and f(x). Always.

The hidden gems in the answer key.

Look for the phrase “initially greater.” That means the function that starts higher, not the one that ends up higher. It’s the difference between being rich at 20 versus rich at 60. Both are good, but the key wants the starting champ.

Another phrase you’ll see: “increasing at a decreasing rate.” Sounds like a paradox, right? It means the function is still growing, but it’s getting tired. Like your motivation at hour three of homework.

If the answer key uses the word “asymptote,” don’t panic. It’s just a fancy way of saying the line gets super close to a boundary but never touches it. Like you and the top shelf of your fridge. So close, yet so far.

Comparing Functions Worksheet Doc

When in doubt, guess and check.

You know what the answer key doesn’t tell you? That guessing is a legitimate strategy. Plug in a number for x, see what happens. Does one function skyrocket while the other mopes? Bingo. You’ve found your answer.

And if your answer differs from the key, don’t assume the key is a liar. Count your own mistakes first. I once argued with a key for ten minutes before realizing I’d read “negative slope” as “positive slope.” The key was right. It always is. Humbling, isn’t it?

Take a break, drink some coffee (or tea, you rebel).

The answer key is a tool, not a judge. It’s there to say, “Hey, you missed that the exponential function beat the linear one at x=4. But hey, you got the y-intercept right! Gold star.”

Now, go back to that worksheet. Look at question 9.5—the one with the two phone plans. One plan is $40 flat fee (linear), the other is $10 plus $5 per gigabyte (also linear, but steeper). The key says the flat fee wins if you use less than 6 GB. That’s literally the answer. You’re welcome.

Final pep talk: comparing functions is just playing detective. You’ve got a chart, a graph, or an equation. You figure out who’s the tortoise and who’s the hare. The answer key hands you the trophy (or tells you to try again). Either way, you win a little knowledge.

Now close that key, take a confident bite of your snack, and tell yourself: “I can compare functions. I am a function-comparing superhero.” Even if your cape is a hoodie. Even if your sidekick is that same caffeinated squirrel. You’ve got this.