Question

The graph of the function f(x) f ( x ) is shown. Both axes of a coordinate grid are shown from negative eight to eight. A line passes through the points (negative four, negative one), (negative three, one), (negative two, three), (negative one, five), (zero, seven) and so on. If g(x)=f(x+3) g ( x ) = f ( x + 3 ) , then select all the statements that are true. The value of g(−5) g ( − 5 ) is 3 3 . The value of g(−1) g ( − 1 ) is 2 2 . The x− x - intercept of g(x) g ( x ) is to the left of the x− x - intercept of f(x). f ( x ) . The x− x - intercept of g(x) g ( x ) is to the right of the x− x - intercept of f(x). f ( x ) . The y y -intercept of g(x) g ( x ) is lesser than the y− y - intercept of f(x). f ( x ) . The y y -intercept of g(x) g ( x ) is greater than the y− y - intercept of f(x). f ( x ) .

Answer 1

Unfortunately, I cannot see the graph you are referring to, as you have not provided it. However, I can provide some general guidance on how to approach the problem.

-To find g(x), we need to shift the graph of f(x) to the left by 3 units. This means that if we want to find g(-5), we need to evaluate f(-5+3) = f(-2). Similarly, to find g(-1), we need to evaluate f(-1+3) = f(2).

-To determine whether the x-intercept of g(x) is to the left or right of the x-intercept of f(x), we need to consider the effect of the shift. If f(x) has an x-intercept at x=a, then g(x) will have an x-intercept at x=a-3. Therefore, the x-intercept of g(x) will be to the left of the x-intercept of f(x).

-To compare the y-intercepts of g(x) and f(x), we need to evaluate g(0) and f(0). If g(0) is less than f(0), then the y-intercept of g(x) is less than the y-intercept of f(x). If g(0) is greater than f(0), then the y-intercept of g(x) is greater than the y-intercept of f(x).

I hope this helps you in determining which statements are true based on the graph and the given information.