0
What else can I help you with?
What does changing the a variable do to quadratic graph?
Changing a variable in a quadratic equation affects the shape and position of its graph. For example, altering the coefficient of the quadratic term (the leading coefficient) changes the width and direction of the parabola, while modifying the linear coefficient affects the slope and position of the vertex. Adjusting the constant term shifts the graph vertically. Overall, each variable influences how the parabola opens and its placement on the coordinate plane.
Is a parabola a graph of a function?
Yes, a parabola can represent the graph of a function, specifically a quadratic function of the form ( y = ax^2 + bx + c ). However, not all parabolic shapes qualify as a function; for instance, if a parabola opens sideways (like ( x = ay^2 + by + c )), it fails the vertical line test, which states that a function must have only one output for each input. Thus, while upward or downward-opening parabolas are indeed functions, sideways-opening parabolas are not.
What is y equals 3x?
I don't understand your question but y=3x is the function of a graph, to graph the function you would plug points into the function such as x=0, x=1, x=-1 and you would find the y values at each point so that you can graph it. In this case the graph is a parabola which has a u shape.
What is a way of determining whether a graph is a function?
For a graph to be a function, each x-value has to take maximum one y-value. One way you can check this is drawing a vertical lines through points on the graph. If a single vertical line intersects the graph in more than one place, that means the x-value defining the line has more than one y-value, and the graph is not a function.tl;dr: Draw vertical lines through the function, and if the lines only intersect the graph once, you have a function.
Is a graph a relation or function?
A graph can represent either a relation or a function, depending on the nature of the relationship between the variables depicted. A relation is simply a set of ordered pairs, while a function is a specific type of relation where each input (or x-value) is associated with exactly one output (or y-value). To determine if a graph represents a function, the vertical line test can be applied: if any vertical line intersects the graph at more than one point, it is not a function.
Always use the vertex and at least points to graph each quadratic equation?
You should always use the vertex and at least two points to graph each quadratic equation. A good choice for two points are the intercepts of the quadratic equation.
Can the graph of a rational function have more than one vertical asymptote?
Assume the rational function is in its simplest form (if not, simplify it). If the denominator is a quadratic or of a higher power then it can have more than one roots and each one of these roots will result in a vertical asymptote. So, the graph of a rational function will have as many vertical asymptotes as there are distinct roots in its denominator.
Is a sign graph a function?
A function must have a value for any given domain. For each edge (or interval), the sign graph has a sign (+ or -) . So, it is a function.
How do you graph and evaluate piecewise functions?
Graph each "piece" of the function separately, on the given domain.
Why does f represent the graph of a function?
Because each vertical lines meets its graph in a unique point.
Is a piecewise graph a function?
Yes, a piecewise graph can represent a function as long as each piece of the graph passes the vertical line test, meaning that each vertical line intersects the graph at most once. This ensures that each input has exactly one output value.
Is the inverse of a quadratic function not a function?
Yes, what you do is imagine the function "reflected" across the x=y line. Which is to say you imagine it flipped over and 'laying on its side". Functions have only one value of y for each value of x. That would not be the case for a "flipped over" quadratic function
What is y equals 3x?
I don't understand your question but y=3x is the function of a graph, to graph the function you would plug points into the function such as x=0, x=1, x=-1 and you would find the y values at each point so that you can graph it. In this case the graph is a parabola which has a u shape.
Which type of graph would you compare the amount of rainfall each month for one year?
A bar graph would be ideal for comparing the amount of rainfall each month for one year as it allows for a clear visualization of the differences in rainfall between each month.
Place the steps to sketch the graph of a rational function in the appropriate order?
answer is:Find the function's zeros and vertical asymptotes, and plot them on a number line.Choose test numbers to the left and right of each of these places, and find the value of the function at each test number.Use test numbers to find where the function is positive and where it is negative.Sketch the function's graph, plotting additional points as guides as needed.
What is used to determined if the graph is a function or not?
There is a method called a vertical line test. A function is defined as a system that has one output for each input. Therefore for every x, there is only one y. So if you draw a vertical line anywhere and you get more than one point that intersects the graph, it is not a function. If it intersects only once, the graph is a function.
What is a way of determining whether a graph is a function?
For a graph to be a function, each x-value has to take maximum one y-value. One way you can check this is drawing a vertical lines through points on the graph. If a single vertical line intersects the graph in more than one place, that means the x-value defining the line has more than one y-value, and the graph is not a function.tl;dr: Draw vertical lines through the function, and if the lines only intersect the graph once, you have a function.
