Every function is a graph. So the only thing is to distinguish functions from other graphs.
One formal convention actually define function as its graph, and a graph is the set of all ordered pairs (x, y)
A function is a special graph where it's set set of all ordered pairs (x, y) where y = f(x). f(x) is unique (or rather one goes in only one comes out), meaning for each x, there is one and only one y. (Note: For each y, there might be many x)
So to test this, we use a "vertical line test". The idea is for all x in the domain of f, say A, we draw a vertical line (x = a for some a in A), it only intersect the graph of f one and only once. Of course, there are infinity many points, you have to do it infinitly many times. Therefore, you can do it generacally:
Let A:= dom f
For all a in A, f is a function if and only if (x = a implies f(x) = f(a) and nothing else)
factors
An equation is the same as a function. Identifying a functional relationship from a graph is nearly impossible unless it is trivially simple like a linear relationship.
A graph represents a periodic function if it exhibits a repeating pattern over regular intervals, known as the period. You can identify this by observing if the graph returns to the same values at consistent distances along the x-axis. Additionally, the function should maintain the same shape and characteristics during each cycle. If you can find a segment of the graph that can be translated horizontally to match itself, it likely indicates periodicity.
The answer depends on what variables are plotted on the graph!
the graph is called a line
-5
You can easily identify the x-intercepts of a graph of a quadratic function by writing it as two binomial factors! Source: I am in Algebra 2 Honors!
To determine the phase constant from a graph, identify the horizontal shift of the graph compared to the original function. The phase constant is the amount the graph is shifted horizontally.
factors
Discriminant = 116; Graph crosses the x-axis two times
The title of a trigonometric graph typically reflects the specific function it represents, such as "Sine Wave," "Cosine Wave," or "Tangent Function." If the graph depicts a sine function, for instance, it may be titled "y = sin(x)." The title helps to identify the type of periodic function and its characteristics, such as amplitude and frequency.
No, a circle graph is never a function.
The relationship between a logarithmic function and its graph is that the graph of a logarithmic function is the inverse of an exponential function. This means that the logarithmic function "undoes" the exponential function, and the graph of the logarithmic function reflects this inverse relationship.
A zero of a function is a point at which the value of the function is zero. If you graph the function, it is a point at which the graph touches the x-axis.
An equation is the same as a function. Identifying a functional relationship from a graph is nearly impossible unless it is trivially simple like a linear relationship.
sine graph will be formed at origine of graph and cosine graph is find on y-axise
Yes the graph of a function can be a vertical or a horizontal line