Question

Use the function transformations to graph the parent function ad the given function on the same coordinate axes

g(x) = 1/4 |x+5| + 2
g(x)= -√1/2x-2

Answer 1

Graph the parent functions f(x) = |x| and f(x) = √x, then apply horizontal shifts, vertical stretches, reflections, and translations according to each function's transformations. Label graphs accordingly and scale axes to fit the given range of x-values from 0 to 20.

Step-by-step explanation:

Graphing the Function Using Transformations

To graph the given functions g(x) = 1/4 |x+5| + 2 and g(x)= -√(1/2x-2) using transformations, you should start by identifying the parent function for each. The parent function for the first equation is f(x) = |x|, and for the second equation, it is f(x) = √x, which are both well-known patterns.

Steps for Graphing the Transformed Functions

1. Begin by graphing the parent functions f(x) = |x| and f(x) = √x on the same coordinate axes.
2. Apply the transformations to the parent functions:
3. For g(x) = 1/4 |x+5| + 2, horizontally shift the graph of |x| five units to the left, vertically stretch it by a factor of 1/4, and then shift it up two units.
4. For g(x)= -√(1/2x-2), stretch the graph of √x horizontally by a factor of 1/2, reflect it over the x-axis, and then shift it down two units.
5. Label the graph with f(x) and x. Scale the x and y axes with the maximum x and y values, keeping in mind the range of x-values given: 0≤x≤20.
6. Plot specific (x,y) data pairs when necessary to get a more accurate graph.

Remember that the y-axis represents the dependent variable and the x-axis represents the independent variable. The general form of a straight-line graph is y = mx + b, where m is the slope and b is the y-intercept.

For each transformed function, sketch the adjusted curves on the coordinates, making sure to clearly differentiate between the parent function and its transformations. This helps visualize the changes made by each transformation.