Which pair of functions could have been used to create the graph of q and w?
A.) q(X) = 18x^2 and w(X) = x^2
B.) q(X) = x^2 + 18 and w(X) = x^2
C.) q(x) = -18x^2 and w(X) = x^2
D>) q(X) = x^2 -18 and w(X) = x^2
To effectively answer this question, we need to know the characteristics of the graph for the functions 'q' and 'w'. However, since the actual graph is not provided, I can give you some general insight about each pair of functions:
A.) q(X) = 18x^2 and w(X) = x^2
- Here, both functions are parabolas facing upwards because their leading coefficients are positive. The graph of q(x) would be much narrower than w(x) because it has a larger leading coefficient.
B.) q(X) = x^2 + 18 and w(X) = x^2
- Both functions are parabolas facing upwards. The only difference is that q(x) is shifted upwards by 18 units. They will have the same shape but different y-intercepts.
C.) q(x) = -18x^2 and w(X) = x^2
- This option has one parabola facing downwards (q(x)) and one facing upwards (w(x)), again with q(x) being steeper due to the larger magnitude of its leading coefficient. So, if one graph is an upward opening parabola and the other is a downward opening parabola, this could be the correct choice.
D.) q(X) = x^2 -18 and w(X) = x^2
- Similarly to option B, both functions are upward-facing parabolas. Here, q(x) is shifted downwards by 18 units. They will have the same shape but different y-intercepts.
Without the graph in question, it's impossible to determine which pair is correct. You would typically look for the following indicators:
- The direction of the opening (upwards or downwards) of the parabolas.
- Any vertical shifts (which would suggest a constant term being added or subtracted).
- The steepness of the parabolae (a larger positive leading coefficient makes the parabola narrower; a negative one flips it upside down).
If you can describe the graph or, even better, provide it, I can give you a more definitive answer.