Determine which of the given functions has a greater rate of change? [A] 𝑦 = 5𝑥 + 2 [B] a function where the input is multiplied by 2.
Determine which of the given functions has a greater rate of change. Our first
function is a linear function. It’s in the form of 𝑦 equals 𝑚𝑥 plus 𝑏, where 𝑚 is your slope and
𝑏 is your 𝑦-intercept. Now the slope is your rate of change, so here the rate of change would be
five or five over one.
Option B says it’s a function where the input is multiplied by two. So
when you have a function, there’s an input and there’s an output. The input is what you plug in.
That’s 𝑥. The output is the answer that pops out. That’s 𝑦. So again, this is a function where the
input is multiplied by two, so 𝑦 equals two 𝑥. This is another linear function, because it’s in
the form 𝑦 equals 𝑚𝑥 plus 𝑏.
Now there isn’t a 𝑏 that just means 𝑏 is zero. So here the rate of change or the slope is two.
So out of either A or B, which one has a greater rate of change? That would be option A: 𝑦 equals five 𝑥 plus two.
Because its rate of change is five over one where B’s rate of change is two over one, which is less.
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