Greetings, today’s post is for those in need of a piecewise functions review! This will cover how to graph each part of that oh so intimidating piecewise functions. There’s x’s, there are commas, there are inequalities, oh my! We’ll figure out what’s going on here and graph each part of the piecewise-function one step at a time. Then check yourself with the practice questions at the end of this post. Happy calculating! 🙂
What are Piece-Wise Functions?
Exactly what they sound like! A function that has multiple pieces or parts of a function. Notice our function below has different pieces/parts to it. There are different lines within, each with their own domain.
Now let’s look again at how to solve our example, solving step by step:
Translation: We are going to graph the line f(x)=x+1 for the domain where x > 0
To make sure all our x-values are greater than or equal to zero, we create a table plugging in x-values greater than or equal to zero into the first part of our function, x+1. Then plot the coordinate points x and y on our graph.
Translation: We are going to graph the line f(x)=x-3 for the domain where x < 0.
To make sure all our x-values are less than zero, let’s create a table plugging in negative x-values values leading up to zero into the second part of our function, x-3. Then plot the coordinate points x and y on our graph.
Ready to try the practice problems below on your own!?
Practice Questions:
Graph each piecewise function:
Solutions:
Still got questions? No problem! Check out the video above or comment below for any questions. Happy calculating! 🙂
Ahoy! Today we’re going to cover the Intersecting Secants Theorem! If you forgot what a secant is in the first place, don’t worry because all it is a line that goes through a circle. Not so scary right? I was never scared of lines that go through circles before, no reason to start now.
If you have any questions about anything here, don’t hesitate to comment below and check out my video for more of an explanation. Stay positive math peeps and happy calculating! 🙂
Wait, what are Secants?
Intersecting Secants Theorem: When secants intersect an amazing thing happens! Their line segments are in proportion, meaning we can use something called the Intersecting Secants Theorem to find missing line segments. Check it out below:
Let’s now see how we can apply the intersecting Secants Theorem to find missing length.
Step 1: First, let’s write our formula for Intersecting Secants.
Step 2: Now fill in our formulas with the given values and simplify.
Step 3: All we have to do now is solve for x! I use the product.sum method here, but choose the factoring method that best works for you!
Step 4: Since we have to reject one of our answers, that leaves us with our one and only solution x=2.
Ready to try the practice problems below on your own!?
Practice Questions: Find the value of the missing line segments x.
Solutions:
Still got questions? No problem! Check out the video above or comment below for any questions and follow for the latest MathSux posts. Happy calculating! 🙂
Greeting math peeps and welcome to MathSux! In this post, we are going to go over 4 ways to Factor Trinomials and get the same answer, including, (1) Quadratic Formula (2) Product/Sum, (3) Completing the Square, and (4) Graphing on a Calculator. If you’re looking for more don’t forget to check out the video and practice questions below. Happy Calculating! 🙂
Also, if you want more Mathsux? Don’t forget to check out our Youtube channel and more below! If you have any questions, please don’t hesitate to comment below. Happy Calculating! 🙂
Hi everyone and welcome to Math Sux! In this post, we are going to look at how to use and applythe median of a trapezoid theorem. Thankfully, it is not a scary formula, and one we can easily master with a dose of algebra. The only hard part remaining, is remembering this thing! Take a look below to see a step by step tutorial on how to use the median of a trapezoid theorem and check out the practice questions at the end of this post to truly master the topic. Happy calculating! 🙂
*If you haven’t done so, check out the video that goes over this exact problem, also please don’t forget to subscribe!
Step 1: Let’s apply the Median of a Trapezoid Theorem to this question! A little rusty? No problem, check out the Theorem below.
Median of a Trapezoid Theorem: The median of a trapezoid is equal to the sum of both bases.Step 2: Now that we found the value of x , we can plug it back into the equation for median, to find the value of median
Want more practice? Your wish is my command! Check out the practice problems below:
Practice Questions:
1.is the median of trapezoid ABCDEF, find the value of the median, given the following:2. is the median of trapezoid ACTIVE, find the value of the median, given the following:3.is the median of trapezoid DRAGON, find the value of the median, given the following:
4. is the median of trapezoid MATRIX, find the value of the median, given the following:
Solutions:
Need more of an explanation? Check out the detailedvideoand practice problems. Happy calculating! 🙂
Today we’re back with Algebra 2, this time solving for radical equations! Did you say “RadicalEquations?” As in wild and crazy equations? No, not exactly, radicals in math are used to take the square root, cubed root, or whatever root of a number.
Example #1:
Radicals are actually pretty cool because we can write them a couple of different ways and they all mean the same thing! Check it out below:Still not sure of their coolness? Let’s see what they look like with actual numbers: Example: Solve the following algebraic equation below for the missing variable (aka, solve for x).Explanation:
How do I answer this question?
The question wants us to solve for x using our knowledge of radicals and algebra. You can also check out how to solve this question on Youtube here!
How do we do this?
Step 1: We start solving this radical equation like any other algebraic problem: by getting x alone. We can do this easily by subtracting 7 and then dividing out 5.
Step 2: Now, to get rid of that pesky radical, we need to square the entire radical. Remember, whatever we do to one side of the equation, we must also do to the other side of the equation, therefore, we also square 14 on the other side of the equal sign. *This gets rid of our radical and allows us to solve for x algebraically as normal!
What happens when there is a cubed root though!?!?
When dividing polynomials with different value roots, raise the entire radical to that same power of root to cancel it out:Remember, we know radicals can also be written as fractions:
Therefore we also know that if we raise the entire radical expression to the same power of the root, the two exponents will cancel each other out:
Example #2:
Want more practice? Try solving radical equations in the next few examples on your own.
Practice:
Solutions:
Looking to brush up on how to solve absolute value equations? Check out the post here! Did I miss anything? Don’t let any questions go unchecked and let me know in the comments! Happy calculating! 🙂
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