Hello! I need help with these 2 questions:
1.) Describe how the graphs of f(x) = |2x| and g(x) = -|2x| are related.
a.) All of these.
b.) The graph of g(x) is a reflection of the graph of f(x) over the y-axis.
c.) Non of these.
d.) The graph of g(x) is a reflection of the graph of f(x) over the x and y axes.
e.) The graph of g(x) is a reflection of the graph of f(x) over the x-axis.
2.) If you use the parent graph y=sqaureroot of x as a reference, how would you graph y=sqaureroot of x-3?
a.) Move the parent graph up three units.
b.) Move the parent graph down three units.
c.) None of these.
d.) Move the parent graph to the right three units.
e.) Move the parent graph to the left three units.
1 reflection
2. shift it right three units.
1.) To determine how the graphs of f(x) = |2x| and g(x) = -|2x| are related, we need to understand the properties of absolute value and the negative sign in these functions.
First, let's consider the graph of f(x) = |2x|. The absolute value function takes the input, 2x, and returns the positive value of 2x for all x-values. This means that no matter if x is positive or negative, the output of |2x| will always be positive.
Now, let's consider the graph of g(x) = -|2x|. The negative sign in front of the absolute value function means that the output will be the negative value of |2x| for all x-values. This means that regardless of whether x is positive or negative, the output of -|2x| will always be negative.
Based on this understanding, let's analyze the given options for the relationship between the graphs of f(x) = |2x| and g(x) = -|2x|:
a.) All of these - Without assessing each option, we cannot determine if all are correct.
b.) The graph of g(x) is a reflection of the graph of f(x) over the y-axis - Considering that the negative sign reflects the graph over the x-axis, this is not accurate.
c.) None of these - Without assessing each option, we cannot conclude that none of them are correct.
d.) The graph of g(x) is a reflection of the graph of f(x) over the x and y axes - Since g(x) = -|2x| reflects the graph of f(x) = |2x| over both the x-axis (due to the negative sign) and the y-axis (because the absolute value function is symmetrical about the y-axis), this option seems valid.
e.) The graph of g(x) is a reflection of the graph of f(x) over the x-axis - This option only considers the reflection over the x-axis but not the y-axis.
Based on the explanations provided, the option that accurately describes the relationship between the graphs of f(x) = |2x| and g(x) = -|2x| is:
d.) The graph of g(x) is a reflection of the graph of f(x) over the x and y axes.
2.) To graph y = square root of (x - 3) by referencing the parent graph y = square root of x, we need to understand the effect of the transformation.
The parent graph y = square root of x is a half-parabola that opens to the right starting from the origin (0, 0). Its key feature is that it intercepts the x-axis at (0, 0) and monotonically increases as x becomes positive.
The transformation y = square root of (x - 3) introduces a shift of three units to the right, horizontally translating the graph. The effect is that the entire graph of y = square root of x is moved three units to the right.
Therefore, the option that accurately describes how to graph y = square root of (x - 3) using the parent graph y = square root of x is:
d.) Move the parent graph to the right three units.