Answer
Step-by-step explanation: Here we are going to explain each statement individually.
Statement 1: "The functions have the same y-intercept"
To find the y-intercept all we need to do is to make x = 0 and calculate or visualize the table.
- As we can see on the table for the first function once x = 0, f(x) = -12 which represents the y-intercept.
- Now all we need to do is to calculate the y-intercept for the second function as follows
As we can see above both functions have the same y-intercept.
Statement 2: "Both functions approach the same value as x approaches ∞"
- First, we can see on the table that the higher the value of x higher is the value of f(x) which means that for the first function once x approaches ∞, f(x) also approaches ∞.
- Now we can calculate as follows to compare with the second function
As we can see above, once x approaches ∞ the first function approach to ∞ and the second function approach zero.
Statement 3: "Both functions approach -∞ as x approaches-∞"
- For the first function we can see in the table that lower is the value of x lower is the value for f(x) and then we can say that the first function approach -∞ as x approaches-∞.
- For the second function we can see below
As we can see above both functions approach -∞ as x approaches-∞
Statement 4: "The functions have the same x-intercept"
- For the first function we just need to visualize the value of x once f(x) = 0 and we can see that the x-intercept is 2.
- For the second function we already know due to our considerations above that once x tends to -∞ g(x) tends to -∞ and once x tends to +∞ g(x) tends to zero but it will never be zero which means g(x) is a function that never touched the x-axis and has no x-intercept.
Statement 5: "Both functions are increasing on all intervals of x"
Due to all our previous observations, we can see that once x increases the value of the functions also increases.
Final answer: The final answer is shown bellow
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