Plz help me solve this ASAP and show the work thank you
1 answer:
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Answer: option a.
Explanation:
A <em>shrink</em> of a function is a <em>shrink</em> on the vertical direction. It means that for a certain value of x, the new function will have a lower value, in the intervals where the function is positive, or a higher value, in those intervals where the function is negative. This is, the image of the new function is shortened in the vertical direction.
That is the reason behind the rule:
- given f(x), the graph of the function a×f(x), when a > 1, represents a vertical stretch of f(x),
- given f(x), the graph of the function a×f(x), when a < 1, represents a vertical shrink of f(x).
So, we just must apply the rule: to find a shrink of an exponential growth function, multiply the original function by a scale factor less than 1.
Since it <em>is a shrink of</em> <em>an exponential growth function</em>, the base must be greater than 1. Among the options, the functions that meet that conditon are a and b:
Now, following the rule it is the function with the fraction (1/3) in front of the exponential part which represents a <em>shrink of an exponential function</em>.
Since each vector is a member of 
, the vectors will span if they form a basis for , which requires that they be linearly independent of one another.
To show this, you have to establish that the only linear combination of the three vectors
that gives the zero vector 
occurs for scalars 
.
Solving this, you'll find that, so the vectors are indeed linearly independent, thus forming a basis for and therefore they must span .
To show this, you have to establish that the only linear combination of the three vectors
Solving this, you'll find that