Hi, I am not the best at math could someone plz help me thank you...
4. Use a graph to determine if the exponential function g( x) = -6 * 5^x is positive or negative and increasing or decreasing.
(A) positive, increasing
(B) positive, decreasing
(C) negative, increasing*****
(D) Negative, decreasing
6. Which of the exponential functions below has a y
-intercept of 2?
(A) f(x)=3^2x
(B) g(x)=3^x+1
(C) h(x)=3^x+2****
(D) j(x)=3*2^x
#4. 5^x is increasing
so, -6*5^x is negative and decreasing
(still increasing in absolute value, but in the negative direction!)
#6. ok
To determine if an exponential function is positive or negative and increasing or decreasing, we can use a graph. Here's how you can do it:
1. Start by choosing a few values for x, such as -2, -1, 0, 1, and 2.
2. Plug those values into the function g(x) = -6 * 5^x to get the corresponding y-values.
3. Plot the points on a graph, with x on the horizontal axis and y on the vertical axis.
4. Connect the points with a smooth curve.
Now, let's analyze g(x) = -6 * 5^x based on the graph:
If the graph is above the x-axis, the function is positive. If it's below the x-axis, it's negative.
If the graph is sloping upwards from left to right, the function is increasing. If it's sloping downwards, it's decreasing.
Based on the graph analysis, we can determine that g(x) = -6 * 5^x is negative (below the x-axis) and increasing (sloping upwards).
Therefore, the correct answer is (C) negative, increasing.