Bethani Gasparine

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. Itโs in the form of ๐ฆ equals ๐๐ฅ plus ๐, where ๐ is your slope and ๐ is your ๐ฆ-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 itโs a function where the input is multiplied by two. So when you have a function, thereโs an input and thereโs an output. The input is what you plug in. Thatโs ๐ฅ. The output is the answer that pops out. Thatโs ๐ฆ. So again, this is a function where the input is multiplied by two, so ๐ฆ equals two ๐ฅ. This is another linear function, because itโs in the form ๐ฆ equals ๐๐ฅ plus ๐.

Now there isnโt a ๐ that just means ๐ 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: ๐ฆ equals five ๐ฅ plus two. Because its rate of change is five over one where Bโs rate of change is two over one, which is less.

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