How to graph y=|x-4| -3

Mathematics

1 answer:

Dafna11 [192]3 years ago

6 0

Okay, let's first establish some ground rules.

1) Whenever something is subtracted or added to x directly, it is a horizontal transformation. In other words, the function is shifted either left or right. Subtraction is right, addition is left.

EX: In y = (x - 4)^2, the function x^2 is moved 4 units to the right.

2) Whenever something is subtracted or added to the whole function, it is a vertical transformation. In other words, the function is shifted either up or down. Subtraction is down, addition is up.

EX: In y = x^2 + 4, the function x^2 is moved 4 units up.

Here, the function |x| is moved 4 units to the right and 3 units down. So, the vertex will be at point (4, -3). Being more technical:

m = -1 if -∞ < x ≤ 4 and m = 1 if 4 < x < ∞

Hope this helps, let me know if I messed up!

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Each student receives one of 4 calculator models and one of 3 types of ruler. How many possible outcomes are there if a student

Tanzania [10]

Answer:

24 possible outcomes

Step-by-step explanation:

Combination has to do with selection. For example, if r object is selected from a pool of n objects, the number if possible ways can be expressed according to the combination formula:

nCr = n!/(n-r)!r!

Applying this in question, if each student receives one of 4 calculator models and one of 3 types of ruler, the number of ways this can be done is:

4C1 × 3C1

4C1 = 4!/(4-1)!1! {If a student gets one calculator)

4C1 = 4×3×2/3×2

4C1 = 4ways

3C1 = 3!/(3-2)!1! {If a student gets a ruler}

3C1 = 3×2/1

3C1 = 6ways

Total number of possible outcomes if a student gets one ruler and one calculator will be 4×6 = 24ways

5 0

3 years ago