To determine if the graph corresponds to the given piecewise function, let's break down the function into its parts.
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For \( f(x) = 2x + 6 \) when \( x < 1 \): This line has a slope of 2 and intercepts the y-axis at 6. It should be graphed for values of \( x \) less than 1.
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For \( f(x) = -\frac{1}{4}x - 3 \) when \( 1 \leq x < 6 \): This line has a negative slope of -1/4 and should start from the point (1, -3) and continue until just before \( x = 6 \).
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For \( f(x) = 4 + 4x \) when \( x \geq 6 \): This line has a slope of 4 and intercepts the y-axis at 4. It should be graphed starting from where \( x = 6 \) onward.
Now, without seeing the actual image, I cannot confirm if the pieces are accurately graphed according to the defined intervals. You will need to compare the characteristics of the graph you've provided against these descriptions.
Since I can't see the graph, my guidance is to check if:
- The first piece ends before \( x = 1 \),
- The second piece starts at (1, -3) and moves towards \( x = 6 \),
- The third piece starts at \( x = 6 \) and has a positive slope going upwards.
If the graph meets all these conditions, the answer would be 1 for yes. If it does not match this criteria, it would be 2 for no.
Please review the graph against this analysis to make your final choice.
1 answer