The table below represents the function f(x). (-6, 12),(-5,-8),(-4,-4), (-3,0),(-2,4),(-1,8),(0,12). If g(x) is a linear function that has a slope of -3 and a y-intercept of -9, which statement is true?
A) The x-intercept of f(x) is less than the x-intercept of g(x). <<<<<<
B) The y-intercept of f(x) is equal to the y-intercept of g(x).
C) The x-intercept of f(x) is equal to the x-intercept of g(x).
D) The y-intercept of f(x) is less than the y-intercept of g(x).
x intercept of f(x) = -3
y intercept of f(x) = 12
g(x) = -3 x -9
x intercept of g(x) = -3
y intercept of g(x) = -9
so it is not A
To determine which statement is true, let's first find the x-intercept of both functions.
The x-intercept of f(x) is the value of x when f(x) equals zero. Looking at the table, we can see that f(x) equals zero at x = -3. So the x-intercept of f(x) is -3.
The x-intercept of g(x) is the value of x when g(x) equals zero. To find this, we can set g(x) = 0 and solve for x. Using the given information, which states that the slope of g(x) is -3 and the y-intercept is -9, we can write the equation g(x) = -3x - 9.
To find the x-intercept, we substitute g(x) with 0 and solve for x:
0 = -3x - 9
3x = -9
x = -3
Therefore, the x-intercept of g(x) is also -3.
Now, looking at the statements:
A) The x-intercept of f(x) is less than the x-intercept of g(x).
We've found that both x-intercepts are -3, so this statement is false.
B) The y-intercept of f(x) is equal to the y-intercept of g(x).
We weren't given the y-intercept of f(x), so we cannot determine if this statement is true or false.
C) The x-intercept of f(x) is equal to the x-intercept of g(x).
We've found that both x-intercepts are -3, so this statement is true.
D) The y-intercept of f(x) is less than the y-intercept of g(x).
Again, we weren't given the y-intercept of f(x), so we cannot determine if this statement is true or false.
Therefore, the correct statement is:
C) The x-intercept of f(x) is equal to the x-intercept of g(x).
To determine the x-intercept of a linear function, we set the value of y to zero and solve for x. The x-intercept is the point where the function crosses the x-axis.
Let's find the x-intercept of g(x), the linear function with a slope of -3 and a y-intercept of -9.
Since the y-intercept is -9, we can write the equation of g(x) as:
g(x) = -3x - 9
To find the x-intercept, we set g(x) to zero and solve for x:
0 = -3x - 9
Adding 9 to both sides:
3x = -9
Dividing both sides by 3:
x = -3
Therefore, the x-intercept of g(x) is -3.
Now, let's analyze the x-intercepts of f(x) which are given as (-6, 12), (-3, 0), and (0, 12). We can see that f(x) crosses the x-axis at x = -6, x = -3, and x = 0.
Comparing the x-intercepts of f(x) and g(x), we find that the x-intercept of f(x) (-3) is less than the x-intercept of g(x) (-6).
Hence, the correct statement is:
A) The x-intercept of f(x) is less than the x-intercept of g(x).