which the following statements is true about the graphs of g(x)=x+5 and h(x)=-g(x)
The true statement is:
The graph of h(x) = -g(x) is the reflection of the graph of g(x) = x + 5 across the x-axis.
Which function's graph is a translation of the graph of f(x)=x shifted 7 units to the left
The function g(x) = f(x + 7) is a translation of the graph of f(x) = x shifted 7 units to the left.
The following statements are true about the graphs of g(x) = x+5 and h(x) = -g(x):
1. The graph of g(x) = x+5 is a straight line with a slope of 1 and a y-intercept of 5. It is a diagonal line that rises from left to right.
2. The graph of h(x) = -g(x) is the reflection of g(x) about the x-axis. This means that h(x) is also a straight line, but it has a slope of -1 (opposite sign of g(x)) and a y-intercept of -5 (opposite sign of g(x)'s y-intercept).
3. The graphs of g(x) and h(x) are parallel to each other because they have the same slope (-1 for both lines).
4. The graphs of g(x) and h(x) intersect at the point (0, -5), as this is the point where g(x) = h(x).
Overall, g(x) and h(x) are linear functions that are related by reflection about the x-axis, resulting in parallel lines with different y-intercepts.
To determine which statement is true about the graphs of g(x)=x+5 and h(x)=-g(x), we need to understand the transformations and properties of these functions.
Let's start by examining the function g(x)=x+5. This is a linear function in the form of y=mx+b, where m represents the slope and b represents the y-intercept. In this case, the slope (m) is 1, and the y-intercept (b) is 5.
The graph of g(x)=x+5 is a straight line that intersects the y-axis at (0, 5). The slope of 1 means that for every unit increase in x, there is a corresponding increase of 1 in y. Therefore, the line goes upward as x increases.
Now, let's consider the function h(x)=-g(x). By replacing g(x) with -g(x) in this equation, we are essentially negating the output of g(x). This means that whatever values g(x) produces, h(x) will produce the negative of those values.
In terms of the graph, reflecting a function over the x-axis negates the y-values. So, the graph of h(x)=-g(x) will be a reflection of the graph of g(x) over the x-axis.
Based on this information, we can analyze the given statements:
1. The graph of h(x)=-g(x) will be an upward-sloping line that intersects the y-axis at (0, -5).
- This statement is not true because the line reflected over the x-axis will have a downward slope and intersect the y-axis at (0, -5).
2. The graph of h(x)=-g(x) will be a downward-sloping line that intersects the y-axis at (0, -5).
- This statement is true because reflecting the line over the x-axis will result in a downward slope, and it will indeed intersect the y-axis at (0, -5).
Therefore, the correct statement is:
- The graph of h(x)=-g(x) will be a downward-sloping line that intersects the y-axis at (0, -5).