Sketch a graph of y = a^x where a is any positive value. Decide true or false for each statement?

a. The graph has one x-intercept.


b. The graph has one y-intercept.


c. The graph passes through the origin.


d. The graph contains points with negative x-coordinates.


e. The graph contains points with negative y-coordinates.Sketch a graph of y = a^x where a is any positive value. Decide true or false for each statement?
T,T,F,T,FSketch a graph of y = a^x where a is any positive value. Decide true or false for each statement?
True:





b.


d.





Explanations:





a. The graph never reaches the x-axis ( sub any value of x into equation to see yourself )


b. The graph of y = a^x ( when there are no transformations ) always intersects the y-axis at ( 0 , 1 ) because when you substitute the value of x = 0, y will always be equal to 1.


c. Answered in part b. ( y-intersect occurs at x = 0 )


d. As your value for y decreases, your value for x must become negative ( think of the rule - to make a power positive, bring it down: x^(-1) = 1/x ) therefore there must be negative values for y to keep decreasing ( it never becomes %26lt;= 0 ).


e. For any value of x, you will never have a negative value for y, negative powers of x just mean smaller values.





Sorry if I have been too specific!