0
OK, so let's call the parent function you're given f(x). There's a series of transformations a parent function can go through:
-f(x) = makes the parent function reflect over the x-axis
On the other hand, f(-x) = makes it reflect over the y-axis
f(x+a) = makes the parent function shift a units to the left
f(x-a) = makes the parent function shift a units to the right
f(x)+a = makes the parent function shift a units up
f(x)-a = makes the parent function shift a units down
f(ax) if x is a fraction like 1/2 , makes the parent function stretch by a factor of 2 (or multiply each x by 2)
f(ax) if x is a whole number (or fractions greater or equal to 1) like 2, makes the parent function compress by a factor of 2 (or divide each x by 2)
a*f(x) if x is a fraction like 1/2, makes the parent function get shorter by a factor of 2 (or divide each y by 2)
a*f(x) if x is a whole number (or fractions greater or equal to 1) like 2, makes the parent function get taller by a factor of 2 (or multiply each y by 2)
One way you can always tell what to do is that everything that is INSIDE the parentheses will be the OPPOSITE of what you think it should do. OUTSIDE the parentheses will do EXACTLY what you think it should do.
And when performing the transformations, start inside the parentheses first and then move outside. For example, f(x-2)+2; move the parent function first to the right 2 units and THEN move it up 2 units.
What else can I help you with?
Which parent function is represented by the graph?
Reciprocal parent function
What are the characteristics of the graph of the reciprocal parent function?
It is a reflection of the original graph in the line y = x.
Which parent function does the graph represent?
f(x)=x^2 apex
What are characteristics of the graph of the absolute value parent function in geometry?
It is in quadrants 1 and 2 It is v shaped it goes through the origin hope this helps!
How can you tell if a graph sHow is a function?
Test it by the vertical line test. That is, if a vertical line passes through the two points of the graph, this graph is not the graph of a function.
Which parent function is represented by the graph?
Reciprocal parent function
What are the advantages of recognizing a function as a transformation of a parent graph before graphing that function?
Recognizing a function as a transformation of a parent graph simplifies the graphing process by providing a clear reference point for the function's behavior. It allows you to easily identify shifts, stretches, or reflections based on the transformations applied to the parent graph, which streamlines the process of plotting key features such as intercepts and asymptotes. Additionally, this approach enhances understanding of how changes in the function's equation affect its graphical representation, making it easier to predict and analyze the function's characteristics.
What are the following functions state the vertex and what transformations on the parent function are needed to make the graph of the given function?
To determine the vertex and transformations of a given function, we first need the specific function itself. For example, if the function is in the form (f(x) = a(x-h)^2 + k), the vertex is ((h, k)). The transformations from the parent function (f(x) = x^2) would include a vertical stretch/compression by factor (a), a horizontal shift (h) units, and a vertical shift (k) units. If you provide the specific function, I can give a more detailed answer.
How do vertical transformations differ from horizontal transformations?
In vertical transformations every point on a graph is shifted upwards by a fixed number of points. In a horizontal transformation, every point on a graph is shifted along the x-axis a certain number of points.
What statements best describes the transformations of the function gx x 4 - 3 compared to its parent graph fx x?
If you want to ask questions about the "following", then I suggest that you make sure that there is something that is following.
What is the linear parent function?
The linear parent function is y=x. The line on a graph passes through the origin(0,0) with a slope of 1. The line will face left to right on the graph like this /.
What are characteristics of the graph of the reciprocal parent function?
It is a hyperbola, it is in quadrants I and II
What are the characteristics of the graph of the reciprocal parent function?
It is a reflection of the original graph in the line y = x.
Which parent function does the graph represent?
f(x)=x^2 apex
How are the two graphs related what transformation occurs?
All of the algebraic transformations occur after the function does its job, all of the rules from the two charts above to transform the graph of a function.
What is the definition of parent graph?
the parent graph of a graph
What is a parent graph?
the graph that is the parent
