![]() ![]() Say one wanted to know the area of a square. Try our quizmaster on this topic by using the link below. This means 104 degrees Fahrenheit is the same temperature as 40 degrees Celsius. We will first do the subtraction, because it is within parentheses. Now, we will use the order of operations to evaluate. Notice that the 'x' was replaced with 104. Consequently, the evaluation process looks like this. This means we want to replace the variable, the 'x,' with 104. ![]() To indicate we want to evaluate the function with the value 104, we write this: If we wanted to know what the Celsius temperature was when the Fahrenheit temperature was 104°, we would need to use this function, where 'x' stands for the Fahrenheit temperature and the 't' stands for the Celsius temperature. We should look at a real problem involving functions. Now, we let the order of operations tell us how to proceed. To do so, we substitute the x-value with -3, like so. If we use f(x) from the section above, we can evaluate the function when the x-value is -3. When we evaluate functions, we replace the variable with values. Try our quizmaster to determine if you know how to tell the difference between a function and a non-function. Notice how a vertical line intersects the sideways parabola twice (below), thereby disqualifying it as a function. However, the parabola that opens sideways is not a function. They are functions because a vertical line intersects the curve no more than once. Likewise, parabolas that face upward and downward are functions, too (see below). If you said ‘V’ and ‘W’ pass the vertical line test, then you are right! A vertical line intersects with them only once, making them functions. The same is true for the ‘D,’ ‘L,’ ‘E,’ ‘H,’ ‘T,’ ‘I,’ ‘R’ and the ‘Y.’ The ‘A,’ ‘C,’ and the ‘Os’ intersect twice with a vertical line, which also disqualifies them from being classified as functions. The ‘M’ fails the vertical line test because a vertical line passes through the right and left sides a countless number of times. The four words are ‘MATH,’ ‘VERY,’ ‘COOL,’ and ‘WILD.’ Can you spot the two letters that pass the vertical line test? The vertical line is in red and the points of intersection are green. Here are some examples using letters of the alphabet. ![]() If the maximum number of intersections is one, then the relation is a function. Look to see how many times a vertical line can intersect the relation. Imagine moving a vertical line throughout the graph. The best way to be able to distinguish these special relations called functions is to use something called the ‘vertical line test.’ Graph the relation. However, some of them are special and we call them ‘functions.’ When we write mathematical expressions, we can graph those expressions. ![]()
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