Look at the function shown in the figure.
When is the function positive?
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Look at the function shown in the figure.
When is the function positive?
The function we see is a decreasing function,
Because as X increases, the value of Y decreases, creating the slope of the function.
We know that this function intersects the X-axis at the point x=-4
Therefore, we can understand that up to -4, the values of Y are greater than 0, and after -4, the values of Y are less than zero.
Therefore, the function will be positive only when
X < -4
What is the solution to the following inequality?
\( 10x-4≤-3x-8 \)
Look at the graph direction! Since this line slopes downward (decreasing), the function is positive to the left of the x-intercept at x = -4.
The line crosses the x-axis at x = -4. For a decreasing function, values are positive before the intercept and negative after. So x < -4 gives positive y-values.
A function is positive when its y-values are greater than zero. On a graph, this means the line is above the x-axis.
Pick a test point! Choose x = -5 (which is < -4). If the function gives a positive y-value at x = -5, then is correct.
Yes! For decreasing functions, positive regions are typically where x is less than the x-intercept. For increasing functions, it's usually where x is greater than the intercept.
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