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A few questions!

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1. The graph of $y=f(x)$ is shown in red below. For how many values of $c$ is $f(c) = -1$? (Assume grid lines are spaced 1 unit apart.)

2. The graph of $y=f(x)$ is shown in red below. Assuming the graph consists of three line segments, what is $f(-2)$?  (Assume grid lines are spaced 1 unit apart.)

3. The graph of $y = h(x)$ is shown in red below. Compute $h(h(7))$. (Assume grid lines are spaced 1 unit apart.)

4. The graph of $y=f(x)$ is shown below in red. Given that $f$ is invertible, find $f^{-1}(4)$. (Assume grid lines are spaced 1 unit apart.)

5. What are the coordinates of the points where the graphs of $f(x)=x^3-x^2+x+1$ and $g(x)=x^3+x^2+x-1$ intersect? Give your answer as a list of points separated by semicolons, with the points ordered such that their $x$-coordinates are in increasing order. (So "(1,-3); (2,3); (5,-7)" - without the quotes - is a valid answer format.)

6. Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $$$\overline{AB}$$$ (meaning the unique line that contains the point $A$ and the point $B$) has $x$-intercept $(-3/2,0)$ and $y$-intercept $(0,3)$. Find $a$ and $b$. Express your answer as the ordered pair $(a,b)$.

7. Find all points $(x,y)$ that are 13 units away from the point $(2,7)$ and that lie on the line $x - 2y = 10$. Give your answer as a list of points separated by semicolons, with the points ordered such that their $x$-coordinates are in increasing order. (So "(1,-3); (2,3); (5,-7)" - without the quotes - is a valid answer format.)

8. Assume that $f(3) = 4$. Name a point that must be on the graph of $y=f(x)+4$.

9. Assume that $f(3) = 4$. Name a point that must be on the graph of $$y=\tfrac12f\left(\tfrac{x}{2}\right)$$.

Jul 22, 2018

#1
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1. The graph of $y=f(x)$ is shown in red below. For how many values of $c$ is $f(c) = -1$?

4 values

Jul 23, 2018
edited by Omi67  Jul 23, 2018
edited by Omi67  Jul 23, 2018
#2
+10441
+1

4. The graph of $y=f(x)$ is shown below in red. Given that $f$ is invertible, find $f^{-1}(4)$.

5. What are the coordinates of the points where the graphs of $f(x)=x^3-x^2+x+1$ and $g(x)=x^3+x^2+x-1$ intersect? Give your answer as a list of points separated by semicolons, with the points ordered such that their $x$-coordinates are in increasing order. (So "(1,-3); (2,3); (5,-7)" - without the quotes - is a valid answer format.)

Jul 23, 2018
edited by Omi67  Jul 23, 2018