What did I learn this week?

This week I learned function notation.

For example: Mapping notation

f is the name, x is the input, and 2x + 3 is the output. If “f : 5 –> 13“, on a graph it would look like this: (5,13), 5 is the input and 13 is the output. That way, it is easy to graph. It would be the same if it looked like this: g : r –> πr². g would still be the name of the function. r would still be the input, and πr² would be the output.

When doing function notation, It will look like this f(x) = 2x + 3. When it says f(x) it does not mean “f multiplied by x” it means “f of x”.

I also learned how to solve Function Notation. For example, this is the equation:

Function g is defined by g(x) = 6 – x².

Evaluate a:  g(4)

To solve this equation we have to put 4 where x is. “g(x)” does not mean g multiplied by x, it means g of x. So, we replace all x’s with 4. It will look like this, “g(4) = 6 – 4²” . Then we multiply the exponent first. So, 4² = 16. Then we calculate the remaining steps. 6-16 = -10. The final answer is g(4) = -10

What did I learn this week?

This week I learned how to find the x and y-intercepts.

For example, we have to find the y-intercept of this equation: 2y + 3x – 12 = 0….. First we replace x with 0 and multiply 3 by 0. Then we are just left with 2y – 12 = 0. We move the -12 to the other side and it will turn into +12. The equation will now look like this: 2y = 0 + 12. After that, we have to simply, so it will look like this: 2y/2 = 12/2. Once it is divided the final answer will be y=6.

The next equation will be to find the x-intercept.

For example, this is the equation: y = 2x – 8… First we make it y(0) and then the equation will simply look like this.. 2x = 8. Then we simply both of the numbers by 2 because we use the number beside the x. Then it will be 2x/2 = 8/2. The final answer is x=4.

What did I learn this week?

This week we reviewed Linear Relations. I learned about the Independent and Dependent Variable.

For example, the Independent variable is the Input, the “x” and the Domain. The Domain is the set of all possible inputs for the function.

Then the Dependent variable. For example, it is the output, the “y” and the range. The range is the set of its possible output values.

This is the equation:  (x = 1,2,3) and (y = 6.20, 12.40, 18.60)…. The input in the equation is x,1,2,3 and the output is y, 6.20, 12.40, 18.60.

What did I learn this week?

This week I was reviewing all the units. I learned something new when completely factoring polynomials.

For example, this is the equation: 9x² + 25… For this equation, it is impossible to factor. So, you just write “cannot factor”. You can’t factor this equation because it’s basically like writing 9x² + 0x + 25 and you would not be able to get to the middle number. To get to +25 it would be +5 multiplied by +5 and if we add those two numbers, it would equal 10 and not 0. Which means we would need one negative number to equal 0.

Another thing I learned was to solve polynomials in fractions.

For example this is the equation: (3x² y) (4x^³ y) ^–²…. For this equation, there is a negative exponent so we will have to turn the equation into a fraction. Then, we make two copies because of the exponent. It will look like this: 3x² y / 4x^³ y • 4x^³ y. Then we multiply the like terms. The final equation will look like this: 3x² y / 16x^⁶ y²..