Thursday, May 28, 2020
Standardized Test Prep The Wisdom of the Blenders
Yes. Yes, it will. As a GRE and SAT tutor in Boston, I find that many of my students have a hard time thinking about functions. What do they mean? What are they like? Even talking about them can be confusing: F of X this, G of Y that. Even though they are hard, students need to be familiar with functions to succeed on the SAT or the GRE. Starting with pre-calculus, math depends more and more on understanding functions. Iââ¬â¢ve found that giving concrete examples helps students retain concepts for SAT math and GRE math tutoring. So, in this blog post, I hope to give an example that sticks in your head. Several years ago Blendtec, a company that sold blenders, became popular for its inventive web advertisements. Traditionally, blenders are a pretty boring part of the consumer-goods market. Mostly, they just turn big chunks of food into little chunks of food. When this company started a new line of more-powerful blenders, they didnââ¬â¢t just say ââ¬Å"it makes ice small in 7.5 seconds while your old blender takes 15 to do it.â⬠Instead, they went for a more memorable approach. To advertise the power of Blendtec blenders, Blendtec started putting out a series of charming 2-minute videos where they asked ââ¬Å"will it blend?â⬠In early episodes, the company tried common items like marbles, hockey pucks, and pens. They all blended. Later, they blended more extreme items like lighters, plungers, or Cheez-Whiz. All liquefied. Eventually, the company started blending iPads, iPhones, and skis. The answer: Yes. No matter what you put into one of these blenders, it gets reduce d to tiny little chunks. Functions are the same way. Say f(x)=2x2+x-4. If you put 3 in, you get 2(3)2+(3)-4 and evaluate 18+3-4=17. If you put in 1, you would get 2(12)+1-4-=2+1-4=-3. Put in x, and get out 2(x)2+(x)-4. Great, it blends. Just like the blender, what you plug into any function comes out looking the same; sort-of. If you put marbles in the blender, you get marble dust. Lighters: lighter dust; iPads: iPad dust. But, like the people at Blendtec, letââ¬â¢s get a little fancier. Given my f(x), what is f(x-4)? To get the answer, follow the same process and plug in (x-4) anytime you see an x. If youââ¬â¢re following along, you should get: 2(x-4)2+(x-4)-4. Then, itââ¬â¢s simply a matter of applying multiplication rules. As a SAT math tutor, I always tell my students to avoid doing too much math at once. Solve the problem in little chunks. Write out 2(x2-4x-4x+16)+(x-4)-4, then distribute through to get 2x2-8x-8x+32+x-4-4. Once youââ¬â¢ve turned your knot of parentheses and coefficients into a simple chain, the expression becomes easy to evaluate: 2x2-15x+24. Seeing function as an appliance that does a specific action to whatever is ââ¬Å"thrown inâ⬠makes learning and using functions easier. For high school students taking the SAT who want to do more math, there will only be more functions as you advance. Talk with a tutor to learn more about functions, how they work, and how frequently they appear in places you wouldnââ¬â¢t expect. Now, after youââ¬â¢ve read all that, you deserve some fun. Go watch the video where they blend lighters. Itââ¬â¢sâ⬠¦illuminating. ;
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